One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091. find the cost of a trumpet, a clarinet would, and a violin.

Answers

Answer 1
Trumpet = $174  Clarinet = $149  Violin = $89    Let's write some equations to express what we know.  2t + 3c + 5v = 1240  3t + 1c + 4v = 1027  5t + 7c + 2v = 2091    So we have 3 unknowns and 3 equations. The 2t and 3t are rather interesting in the 1st 2 equations since the 3rd equation has 5t. So if we subtract the 1st and 2nd equations, we can cancel out the t values. So   5t + 7c + 2v = 2091  -( 3t + 1c + 4v = 1027)  = 2t + 6c - 2v = 1064  -(2t + 3c + 5v = 1240)  = 3c - 7v = -176    Now we can express c in terms of v.  3c - 7v = -176  3c = 7v - 176  c = (7/3)v - 58 2/3    Substitute the expression (7/3)v - 58 2/3 for c in the expression 2t + 3c + 5v = 1240 giving  2t + 3((7/3)v - 58 2/3) + 5v = 1240    and solve for t, first distribute the 3  2t + 7v - 176 + 5v = 1240    Merge the v terms  2t + 12v - 176 = 1240    Add 176 to both sides  2t + 12v = 1240 + 176 = 1416    Subtract 12 v from both sides  2t = 1416 - 12v    Divide both sides by 2  t = 708 - 6v    Now substitute both 708 - 6v for t and (7/3)v - 58 2/3 for c in 3t + 1c + 4v = 1027 and solve for v  3t + 1c + 4v = 1027  3(708 - 6v) + (7/3)v - 58 2/3 + 4v = 1027    Distribute the 3  3(708 - 6v) + (7/3)v - 58 2/3 + 4v = 1027  2124 - 18v + (7/3)v - 58 2/3 + 4v = 1027    Combine terms  2065 1/3 - (11 2/3)v = 1027    Subtract 2065 1/3 from both sides   -(11 2/3)v = 1027 - 2065 1/3 = -1038 1/3    Divide both sides by -11 2/3  v = 89    So we know the violins cost $89 each.  Plugging that value into the formula t = 708 - 6v which we created earlier  t = 708 - 6v  t = 708 - 6 * 89 = 708 - 534 = 174    So we know that a trumpet costs $174  Now plug the price of a violin into the formula c = (7/3)v - 58 2/3 to get the cost of a clarinet.  c = (7/3)v - 58 2/3  c = (7/3)89 - 58 2/3 = 207 2/3 - 58 2/3 = 149    And a clarinet is $149    Let's verify  2t + 3c + 5v = 2*174 + 3*149 + 5*89 = 348 + 447 + 445 = 1240  3t + 1c + 4v = 3*174 + 1*149 + 4*89 = 522 + 149 + 356 = 1027  5t + 7c + 2v = 5*174 + 7*149 + 2*89 = 870 + 1043 + 178 = 2091    All the expressions match what was given, so the prices are  Trumpet = $174  Clarinet = $149  Violin = $89

Related Questions

David charges $15 plus $5.50 per hour to mow lawns Arie charges $12 plus $6.25 per hour to mow lawns. In what situation is Aries charge greater than or equal to David’s charge?

Answers

Aries's charge will be greater than it equal to David's charge if they are charging to mow for 4 or more hours.

8 hundreds 4 tens = 84 blank

Answers

8 hundreds and 4 tens equals 840

Andy runs 436.8 meters in 62.08 seconds. I’d Andy runs at a constant speed, how far does he run in one second? Give you answer to the nearest tenth of a second.

Answers

436.8  m......62.08 s
x m........1 s
(436.8 X 1) / 62.08 = 7.03 m/s
7.03 m.... 1 s
y m.....1/10 s
(7.03 X 0,1 ) /1=0,703 m




how are the perimeters of two similar figures related?

Answers

they have the same ratio.
imagine 2 similar triangle, the first one has one side of 8cm and another side with 10cm
the second triangle is one side 4 cm and other side of 5cm
the ratio of side of each similar triangle is the same
4/8 = 5/10 = 1/2

How to simplify each expression
2/3(7w + 4) - 1/3 (2w - 1 )

(3-7m) +2(3.5m+ 1)

Answers

  14 w /3  + 8/3  - ( 2/3w  -1/3 )   =  
14w/3  + 8/3 -2/3 w +1 /3 = 

12w /3  + 9/ 3 = 3  ( 4w +3) / 3  =  4w +3  

the second 
 3-7m +7m+ 2 = 5 





tickets to the local basketball arena cost $54 for lower bowl seats and $20 for upper bowl seats. A large group purchased 123 tickets at a cost of $4,262. How many of each type of ticket did they purchase? help me please i nee the answer and can you please explain too

Answers

4,262 / 54 =78.9. So they got 77 lower bowl seats
123-77= 46 upper bowl seats

The number of  lower bowl seats an upper bowl seats tickets to the local basketball arena bought by group is 53 and 70 respectively.

What is system of equation?

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

Tickets to the local basketball arena cost $54 for lower bowl seats and $20 for upper bowl seats. A large group purchased 123 tickets at a cost of $4,262.

Let the number of lower bowl seats purchased by group is x and upper bowl seats is y. As number of ticket purchased is 123. Thus,

[tex]x+y=123[/tex]        

Solve it further,

[tex]x+y=123\\x=123-y[/tex]             ....1

The total cost of ticket is 4262. Thus,

[tex]54x+20y=4262[/tex]

Put the value of x in this equation,

[tex]54(123-y)+20y=4262\\6642-54y+20y=4262\\-34y+20y=4262-6642\\-34y=-2380\\y=\dfrac{2380}{34}\\y=70[/tex]

Put this value in equation 1,

[tex]x=123-70\\x=53[/tex]

Thus the number of  lower bowl seats an upper bowl seats tickets to the local basketball arena bought by group is 53 and 70 respectively.

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I ALREADY SET UP THE GRAPH, I JUST NEED TO KNOW WHAT TO DO NEXT!

During swim practice, an Olympic swimmer is required to complete three swimming intervals, in this order: warm-up freestyle, sprint freestyle, and cool-down breast stroke. After he completes each interval, he rests for three minutes.
Sketch a graph that represents the swimmers’ interval times with respect to swimming speed. Assign the x- and y-axes with appropriate labels. You may use description words instead of numbers to label the graph

Answers

Final answer:

After labeling and scaling the axes on your graph to represent the swimmer's interval times with respect to swimming speed, construct a histogram with bars for each workout interval and denote rest periods. Use a ruler for precision and clarity in your graph.

Explanation:

Once you have set up your graph to represent the Olympic swimmer's interval times with respect to swimming speed, the next steps are:

Label the x-axis with 'Time (min)' because this is the independent variable, and scale it appropriately. Considering that the intervals occur every few minutes and there are rest periods, number the x-axis from 0 to 70 minutes with a tick mark every 10 minutes.For the y-axis, choose a label such as 'Swimming Speed' and decide on a unit that makes sense for your data. The scale should begin at 0 and should be high enough to include the swimmer's fastest speeds. Scales are often made with consistent intervals such as every 1 unit or every 5 units, depending on the range of data.Construct a histogram to visually represent the swimmer's speeds during the intervals. Each bar will show the average speed during a specific interval. Make sure to use a ruler for neatness and accuracy.Consider including three distinct histogram bars for each of the swimming intervals -- warm-up, sprint, and cool-down -- with the heights corresponding to the average speeds of these intervals.Don't forget to mark the rest periods between the intervals. These could be represented by gaps or separate annotations on the x-axis to denote the 3-minute rest times.Finally, ensure the histogram is clear, with each interval and rest period accurately represented in your scaled graph.

Final answer:

To sketch a graph representing the swimmer's interval times with respect to swimming speed, start by labeling the axes with Time (min) and Interval Time (min). Then, determine the appropriate scale for each axis. Plot the interval times on the graph and connect the points with lines.

Explanation:Step 1: Label the graph

Label the x-axis as Time (min) and the y-axis as Interval Time (min).

Step 2: Determine the scale

For the x-axis, number the axis from 0 to 70 minutes with a tick mark every 10 minutes. For the y-axis, use a scale from 0 to 160 minutes with a tick mark every 10 minutes.

Step 3: Plot the intervals

Using the information given, plot the interval times on the graph. Start with the warm-up freestyle, then the sprint freestyle, and finally the cool-down breast stroke. Each interval time should be represented on the y-axis.

Step 4: Connect the points

Connect the plotted points for each interval with a line. This will represent the swimmer's interval times with respect to swimming speed.

PLease help ME!!!!!!!!!!!!!!!!!!


Conduct a poll of adults and students in your area. Ask them how much time they spend online each week that is not for work or school. Describe how you conducted the poll and record the results of the poll in an organized manner below.

Answers

Most of the adults in my community spend 43% of their time online that is not used for work or school.

And most of the children in my Community spend 53% of their time online without working.

how do you simplify -7 |7|

Answers

Negative 7 times the absolute value of 7
negative times a positive is a negative
so -7*7= -49
The answer is:  " - 49 " .
_____________________________
The problem:  "What is "-7" multiplied by "the absolute value of (7)"?

Note:  The absolute values of (7) = 7 ; that is the absolute values of (positive 7) is:  "(positive 7)" .
__________________________
  So, we are left with:  What is: "-7 " multiplied by  "+ 7" ; 
           {i.e. ,  " (-7)*(7) = ? " } ;
_________________________
The answer is:  " -49 " .
_________________________

Carly has 2 more nickels than dimes in her pocket. She has 40 cents. How many nickels does Carly have How many dimes does Carly have? Show your work.

Answers

She has 2 dimes and 4 nickels.
Knowing dimes equal 10 cents, if you have 1 dime and 3 nickels, you’d have 20 cents, 2 dimes and 4 nickels you’d have 40 cents. You have to have two more nickels than dimes.

Carly has 2 nickels and 4 dimes if Carly has 2 more nickels than dimes in her pocket. She has 40 cents.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Carly has 2 more nickels than dimes in her pocket. She has 40 cents.

Let x be the number of nickels  Carly has and y be the number of dimes Carly has.

5(x + 2) + 10x = 40

5x + 10 + 10x = 40

15x = 30

x = 2 nickles

y = x + 2 = 2 + 2 = 4 dimes

Thus, Carly has 2 nickels and 4 dimes if Carly has 2 more nickels than dimes in her pocket. She has 40 cents.

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A truck driver drove 120 miles in 1 3/4 hours what is the speed of the truck in miles per hour

Answers

20 would be the correct
answer

its 120mi÷1.75hours=68.6miles per hour

Circle the ordered pairs that are solutions to the inequality y - 2x < - 1.

(1, 0)
(0, 1)
(0, -1)
(-1, 0)
(3, 2)
(-2, -4)
(2, 4)
(-4, 2)
(0, 0)

Please help!

Answers

All we have to do, is plug in the ordered pairs, and see which ones are true to the equation. (x,y)

(1,0) After plugging those into the equation we get: 2<-1. this is not true, so this answer is false.

I continued this all the way down the line:

(0,1)= 1<-1 = false
(0,-1)=-1<-1=false
(-1,0)= -2<-1=true
(3,2)=-1<-1=false
(-2,-4)=2<-1=false
(2,4)=2<-1=false
(-4,2)=8<-1=false
(0,0)=0<-1=false

There is only one true ordered pair for this equation:

(-1,0)


what is 0.13 +(-5.7)

Answers

The correct answer would be -5.57

Salama makes fruit baskets with oranges and bananas. She uses between 8 and 16 oranges and bananas in a ratio of 3 oranges to 2 bananas. Drag the correct number of fruit into the box to meet these requirements.

Answers

Answer:

[tex]\frac{6 \ oranges }{4 \ bananas}[/tex] and [tex]\frac{9 \ oranges}{6 \ bananas}[/tex]

Step-by-step explanation:

An image is missing here. However, using the given ratio we can find different  representations of fruits.

We know that the ratio between oranges and bananas is

[tex]\frac{3 \ oranges}{2 \ bananas}[/tex]

So, if she uses between 8 and 16 oranges and bananas, we can only use ratios that fall between this numbers.

Some ratios that represent this situation are

[tex]\frac{6 \ oranges }{4 \ bananas}[/tex] using 10 oranges and bananas.

[tex]\frac{9 \ oranges}{6 \ bananas}[/tex] using 15 ranges and bananas.

This two ratios are the ones that can be used, because other ratios don't fall between the interval (8,16).

Therefore, the valid ratios here are

[tex]\frac{6 \ oranges }{4 \ bananas}[/tex] and [tex]\frac{9 \ oranges}{6 \ bananas}[/tex]

Answer:

9 orange

6 bananas

Step-by-step explanation:

It takes 37 pounds of seed to completely play a 4 acre field how many acres can be planted per pound of seed

Answers

4 acres ÷ 37 pounds 
.108 acres per pound

Calvin Butterball is driving along the highway. He starts up a long, straight hill. 114 meters from the bottom of the hill Calvin's car runs out of gas. He doesn't put on the brakes, so the car keeps rolling for awhile, coasts to a stop, then start rolling backwards. He finds that his distances from the bottom of the hill 4 and 6 seconds after he runs out of gas are 198 and 234 meters, respectively. b.Write an equation expressing Calvin's distance from the bottom of the hill in terms of the number of seconds which have elapsed since he ran out of gas.

Answers

Final answer:

To determine Calvin's distance from the bottom of the hill in terms of the number of seconds since running out of gas, we can use the equation of motion for uniformly accelerated motion.

Explanation:

To write an equation expressing Calvin's distance from the bottom of the hill in terms of the number of seconds that have elapsed since he ran out of gas, we can use the equation of motion for uniformly accelerated motion.

Calvin's initial position at 0 seconds is 114 meters, and his final position at 4 seconds is 198 meters. Plugging these values into the equation:

d = vi x t + 0.5 x a x t²

we can solve for the acceleration, a:

a = (d - vi x t) / (0.5 x t²)

Substituting the values of d = 198m and t = 4s, we get:

a = (198m - 114m) / (0.5 x (4s)²)

After obtaining the acceleration, we can use the equation to find Calvin's distance from the bottom of the hill at any time after running out of gas.

what number is midway between 1/7 and 1/5. show your work

Answers

Answer: Convert to equivalent fractions with a common denominator and then choose a suitable numerator between the ones you have calculated.


Answer: 0.17142857142

- Subtract .2 by .142857142
You get
0.05714285714

divide
0.05714285714 by 2
=
0.02857142857

add .142857142 to 0.02857142857

you should get an answer

find the sum of the first 13 terms in the series -5+1+7...+67

Answers

this is an arithmetic series with common difference 6 

S13  = (13/2)[2*-5 + (13-1)*6)]  =  403

Tasha finished the first draft of her history essay. The teacher said it had to be at least six hundred words long. She counted in her draft and found she had 369. How many more words does she need to meet the minimum words count for the assignment?

Answers

the answer would be 231 because 600-369=231

james scored 300 runs in cricket. he requires 900 runs to qualify for league MVP contention. he scores 50 runs during the average of the game. how many games does he have to plsy to score the remaining runs he needs?

Answers

He would need to play 12 average scoring games.
900 (goal) - 300 (has) = 600
and 600/50 is 12 
hope this helps :)

James needs to score a total of 900 runs for MVP contention. Subtracting the 300 runs he has already made from the 900 required leaves 600 runs. By dividing these 600 remaining runs by his average of 50 runs per game, we find that James needs to play 12 more games.

James currently scored 300 runs and needs a total of 900 runs for MVP contention. To find out how many more games he must play, we need to calculate the remaining runs required and divide that number by the average runs he scores per game. The remaining runs needed are 900 - 300, which equals 600. As James scores an average of 50 runs per game, we divide the remaining runs, 600, by 50 to find the number of games he needs to play.

600 ÷ 50 = 12 games

Therefore, James will need to play 12 more games to score the remaining runs he requires for league MVP contention.

3(x+1)-2(3x+7) i need help with this question

Answers

First distribute

3x + 3 - 6x - 14

Simplify 

-3x - 11

solve for x

-3x  = 11

-3x/-3 = 11/-3

x = -11/3

hope this helps
3(x + 1) - 2(3x + 7)

3x + 3 - 6x - 14

(3x - 6x) + (3 - 14)

-3x - 11

hope this helped, God bless!

A sheet of plywood was made by gluing 7 sheets of wood together.
2 of the sheets were 0.0625 inch thick and the rest were 0.125 inch thick.
how thick was the plywood?

Answers

We can use the equation y=2(0.0625)+5(0.125), y being the thickness of the plywood.
I got 5(0.125) because two sheets of the 7 were already used, meaning there are 5 sheets of plywood left over.
y=0.125+0.625
y=0.75
Therefore, the plywood is 0.75 inches thick.

Which symbol correctly compares the two fractions? Use > , < , or =. Enter your answer in the box. 2/4 3/8

Answers

The greater than symbol, ">," accurately compares the two fractions because 2/4 > 3/8. They are 2/4 and 3/8, respectively.

what are symbols ?

something that represents another item. especially: something tangible that denotes or implies something else that is not itself imaginable or demonstrable. The lion is a representation of bravery. an alternative to a word or combination of words, such as a letter, character, or sign.

given

= 2/4 = 0.5

= 3/8 = roughly 0.37

The greater than symbol, ">," accurately compares the two fractions because 2/4 > 3/8.

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Final answer:

To compare 2/4 and 3/8, simplify 2/4 to 1/2, then convert to eighths, resulting in 4/8. Since 4/8 is greater than 3/8, 2/4 is greater than 3/8.

Explanation:

To compare the fractions 2/4 and 3/8, we need to find a common denominator or convert them to a common form such as decimals.

The simplest way is to notice that 2/4 can be simplified to 1/2.

Now, if we convert 1/2 to eighths, we get 4/8 because we multiply both the numerator and denominator by 4 to get the common denominator of 8 (1 x 4)/(2 x 4) = 4/8.

Comparing 4/8 with 3/8, we can see that 4/8 is larger than 3/8, as 4 is greater than 3.

Hence, the correct inequality symbol to compare 2/4 and 3/8 is ">".

According to the transitive property of inequality which states that if a > b and b > c then a > c, if 4/8 > 3/8 and 2/4 is equal to 4/8, then 2/4 > 3/8.

Solve for x. -16 = 8x/5
x = 10
x = -10
x = -25

Answers

- 16 = 8x/5

solve equations



step 1 simplify both sides of the equation.

- 16  = 8/5x



step 3 flip the equation

8/5x = - 16


step 3 multiply both sides by 5/8

( 5/8) * ( 8/5x) = (5/8) * ( - 16)

x = - 10


answer x = - 10

two angles are supplementary if the sum of their measures is 180 degrees. find two supplementary angles such that the smaller is 30 degrees more than one-half of the larger.
step by step please

Answers

If the larger angle is x and the smaller angle is y, y=(1/2)x+30 since it's 30 more than 1/2 of it. In addition, x+y=180 since they are supplementary. Plugging y=(1/2)x+30 into that, we get x+x/2+30=180=1.5x+30. Subtracting 30 from both sides, we get 1.5x=150. Next, we can divide both sides by 1.5 to get x=100 and y=(1/2)*100+30=50+30=80

Tony spent $11.52 for some pens that were on sale for $.72 each how many pens did Tony bye

Answers

he will bye 16 pens hope that helps u

What is the unit price for thecans

Answers

Greetings!

First Poster:
9/2=4.5
4.5/24=0.1875
One can would cost approximatly 0.19 dollars at the first store.

Second Poster:
10/4=2.5
2.5/12=0.208333333
One can would cost approximately 0.21 dollars at the second store.

Third Poster
9/3=3
3/12=0.25
One can would cost 0.25 dollars at the third store.

The first store has the best value for lemonade.

Hope this helps.
-Benjamin

Please help. I don't know how to answer this.

Answers

 the train route (5,13)

is it possible for number to be a rational number that is not an integer but is a whole number explain

Answers

see above
let me know if you have any questions :-)

how to solve cube roots

Answers

you times the number by its self 3 times for ex. you have 4 ^cubed it would be 4*4*4=64

Final answer:

To solve cube roots, follow these steps: estimate, test, adjust, refine, and round the final answer.

Explanation:

To solve cube roots, you need to find the number that, when multiplied by itself three times, gives you the original number. Here are the steps:

Start with the cube root symbol (∛) and the number you want to find the cube root of.Estimate the cube root by finding a number that, when cubed, is close to the original number.Test your estimate by cubing it and comparing it to the original number.If your estimate is too high or too low, adjust it and repeat the testing step.Once you have a good estimate, refine it by using a calculator or a computer program.Round the final answer to an appropriate number of decimal places.
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