A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 469 tickets overall. It has sold 112 more $20 tickets than $10 tickets. The total sales are $8300 How many tickets of each kind have been sold?
Final answer:
The basketball team has sold 155 $10 tickets, 267 $20 tickets, and 47 $30 tickets. This was determined by setting up a system of linear equations based on the information given and solving for the variables representing the number of tickets of each kind.
Explanation:
The problem at hand is a classic example of a system of linear equations in the world of numerical problems. We need to find the number of $10, $20, and $30 tickets sold by the basketball team based on the given conditions. Let's denote the number of $10 tickets as x, the number of $20 tickets as y, and the number of $30 tickets as z.
The total number of tickets sold is 469: x + y + z = 469.The team has sold 112 more $20 tickets than $10 tickets: y = x + 112.The total sales amount to $8300: 10x + 20y + 30z = 8300.Substituting y from the second equation into the first and third equations, we get two new equations:
x + (x + 112) + z = 469, which simplifies to 2x + z = 357.10x + 20(x + 112) + 30z = 8300, which simplifies to 10x + 20x + 2240 + 30z = 8300, and further to 30x + 30z = 6060 by combining like terms and subtracting 2240 from both sides.Dividing the last equation by 30, we obtain x + z = 202. Now, we have a system of two equations with two variables:
2x + z = 357x + z = 202Subtracting the second equation from the first, we find x = 155. We can then substitute x into the second equation to find z = 202 - 155 = 47.
Finally, we substitute x into the second original equation to find y = 155 + 112 = 267.
Therefore, the team has sold 155 $10 tickets, 267 $20 tickets, and 47 $30 tickets.
Answer to this problem
will give BRAINEST
Use the elimination method to solve the system of equations. Choose the correct ordered pair.
Exact product of 379 and 8
What fraction of £2 is 50p
A mail truck traveled 82 miles in 412 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?
Answer:
18.2
Step-by-step explanation:
The equation d = can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V?
dm = V
= V
= V
m – d = V
The equivalent equation solving for volume is v = mass/density
Data;
Mass = mdensity = dvolume = volumeDensity of an ObjectThe density of an object can be calculated using the formula
[tex]density = \frac{mass}{volume}[/tex]
Making the volume the subject of formula here
[tex]density = \frac{mass}{volume}\\ volume = \frac{mass}{density}[/tex]
The equivalent equation solving for volume is v = mass/density
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If Argyl earns $93.00 for 7.75 hours of work, how many must he work to earn $571.50?
the area of the top face of a cube is 9 meters. what is the volume? {I need to know how to actually do this}
-4(c)+5=-6-30????????????????
which of the following describes a simple event ?
A. Tossing a coin 5 times and getting heads twice
B. spinning "back 2spaces" on a spinner
C. Spinning “back 2 spaces” on a spinner and drawing a blue or red marble from a box
D. Rolling an odd number on a die and getting tails on the toss of a coin
Option B, spinning "back 2 spaces" on a spinner, describes a simple event as it represents a single outcome from the experiment, in contrast to the other options which describe compound events.
A simple event is an event that consists of a single outcome of an experiment. When tossing a coin 5 times and getting heads twice, we're looking at a compound event because it involves a combination of outcomes. In the options given, option B, spinning "back 2 spaces" on a spinner represents a simple event because it describes a single outcome that can occur from the experiment. The other options involve multiple outcomes or combinations and are therefore not simple events.
Considering the additional information provided:
Coin tosses and the outcomes of 5 coin tosses just give us a set of possible results which help illustrate compound events. The idea of grouping real world observations into outcomes or events shows us that a simple event is a single, specific outcome, such as getting an even number when rolling a die, which can be defined as an event with a single characteristic and has a calculable probability.
what is 165% written as a decimal and fraction
If candies have a cost X cents less per dozen, it would have cost 3 cents less for x+3 candies then if they had cost x cents more per dozen. What is x?
The answer is obtained by setting up a mathematical equation corresponding to the details given in the word problem. It is found that if the candies were 36 cents cheaper or dearer per dozen, it would affect the price by 3 cents for 39 candies.
Explanation:The problem can be solved by translating the words into a mathematical equation. Let's denote the original price of a candy as Y cents. Therefore, a dozen candies would cost 12Y cents.
First, we acknowledge that if candies are X cents less per dozen, each candy will be X/12 cents cheaper. And if you buy x+3 such candies, you will pay (x+3)*X/12 cents less.
Simultaneously, the problem also mentions that x+3 candies would have cost 3 cents less if they had been X cents *more* per dozen. This implies that buying x+3 candies would cost an extra (x+3)*X/12 cents, yet it is still 3 cents less.
Therefore, these two costs should be equal: (x+3)*X/12 = (x+3)*X/12 +3. By solving this equation: X = 36. Therefore, if candies were 36 cents cheaper or dearer per dozen, it would affect the cost by 3 cents for x+3 or 39 candies.
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A rectangular lot with a 50-ft frontage and a 230-ft depth sold for $8625. Find the cost of the lot per square foot
What is the sum of the geometric series in which a1 = 4, r = 3, and an = 324?
Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.
The sum of the geometric series is approximately 324.
Explanation:The sum of a geometric series can be found using the formula:
Sn = a1(1 - rn) / (1 - r)
Where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.
Plugging in the given values, we have:
Sn = 4(1 - 3n) / (1 - 3)
Now we can solve for n by plugging in the given value of an:
324 = 4(1 - 3n) / (1 - 3)
Cross-multiplying and simplifying:
324(1 - 3) = 4(1 - 3n)
324 - 972 = 4 - 12n
-648 = -8n
Dividing both sides by -8, we get:
81 = 2n
Taking the logarithm base 2 of both sides:
n = log2(81)
Using a calculator, we find that n is approximately 6.3398.
Now we can plug this value back into the formula:
Sn = 4(1 - 36.3398) / (1 - 3)
Simplifying further:
Sn ≈ -648 / -2
Sn ≈ 324
20d + 13 - 12d = -14
20d +13 -12d = -14
combine like terms
20d-12d = 8d
8d+13 = -14
subtract 13 from each side:
8d =-27
divide both sides by 8
d = -27/8
Niko bought 4 stamps each week for 3 weeks. He wants to put 6 stamps on each page of his album how many pages will niko use
Write the quadratic equation in factored form. Be sure to write the entire equation. x2 - 5x - 24 = 0
Answer:
(x+3)(x-8)
Step-by-step explanation:
What is the solution of the system? Use substitution. x = –2y + 10 –6y = 6x – 6 z = –3x + 10y
To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y. We'll substitute this expression for x in the other two equations to find the values of y and z.
Explanation:To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y: x = -2y + 10. We'll substitute this expression for x in the other two equations to find the values of y and z. Substituting -2y + 10 for x in the second equation, we have -6y = 6(-2y + 10) - 6.
Simplifying this equation, we get y = -2. Substituting y = -2 in the first equation, we find x = -2*(-2) + 10 = 14. Finally, substituting x = 14 and y = -2 in the third equation, we find z = -3*14 + 10*(-2) = -52.
Decimals from 7.0 to 8.4, with an interval of 0.2 between each pair of decimals
help me
2y = x + 2
x – 3y = –5
what is 1.086 rounded to the nearest whole number
what's the property of 34+0+18+26
the price of a technology stock was $9.53 yesterday. Today, the price rose to $9.66. Find the percentage increase. Round your answer to the nearest tenth of a percent.
give an example of an addition problem in which you would and would not group the addends differently to add
Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Write and solve an inequality to solve for the least amount of money he needs to deposit to avoid a fee.
in how many ways can 5 men and 5 woman sit alternately in a row of 10 seats?
the men can be arranges in 5! ways
and the women in 5! ways
so (5*4*3*2) = 120
120 *120 = 14,400 ways
Sorry if I'm bothering you! But can you guys figure out this problem for me? "A car travels at 65 miles per hour. Going through Construction, it travels 3/5 this speed. Write this fraction as a decimal and find the speed.
Thanks,
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Paulita reads an average of 20 pages each day. She has 6 days to read 100 pages. Will she finish her reading in 6 days? Explain
The diagram shows a rhombus ABCD. The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis. The mid-point of BD is M. Find, by calculation, the coordinates of each of M, A and C.
The coordinates of the midpoint M, point A, and point C in the rhombus can be found using formulas. The coordinates of M are (4, 6), the coordinates of A are (0, 0), and the coordinates of C are (4, 2).
Explanation:To find the coordinates of the midpoint of BD, we can use the midpoint formula:
M = ( (x1+x2)/2, (y1+y2)/2 )
Substituting the coordinates of B and D into the formula, we get:
M = ( (2+6)/2, (10+2)/2 )
Simplifying, we get:
M = (4, 6)
Since A lies on the x-axis, its y-coordinate is 0. Therefore, the coordinates of A are:
A = (0, 0)
To find the coordinates of C, we can use the fact that a rhombus has opposite sides equal in length and parallel. Since B and D have the same y-coordinate, the y-coordinate of C will also be the same. The x-coordinate of C will be the average of the x-coordinates of B and D. Therefore, the coordinates of C are:
C = ( (2+6)/2, 2 )
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