Suatu jenis roti memerlukan 150 gram tepung dan 50 gram mentega. Roti jenis lain memerlukan 75 gram tepung dan 75 gram mentega, produksi roti membuat sebanyak roti dan dua jenis roti itu. Bahan yang tersedia 2.250 gram tepung dan 1.250 gram mentega, berapakah banyak roti masing masing yang dibuat?
Answers
The second type of the bread be bread B
Let the flour be 'f' and the butter be 'b'
We need 150f + 50b for bread A and 75f + 75b for bread B
We can compare the amount of flour and bread needed for each bread and write them as ratio
FLOUR
Bread A : Bread B
150 : 75
2 : 1
We have a total of 2250gr of flour, and this amount is to be divided into the ratio of 2 parts : 1 part. There is a total of 3 parts.
2250 ÷ 3 = 750 gr for one part then multiply back into the ratio to get
Bread A : Bread B = (2×750) : (1×750) = 1500 : 750
BUTTER
Bread A : Bread B = 50 : 75 = 2 : 3
The amount of butter available, 1250 gr is to be divided into 2 parts : 3 parts.
There are 5 parts in total
1250 ÷ 5 = 250 gr for one part, then multiply this back into the ratio
Bread A: Bread B = (2×250) : (3×250) = 500 : 750
Hence, for bread A we need 1500 gr of flour and 500 gr of butter, and for bread B, we need 750 gr of flour and 750 gr of butter.
The amount of Bread Type 1 is 10 pieces
The amount of Bread Type 2 is 10 pieces
Further explanationSimultaneous Linear Equations can be solved using one of the following methods :
Elimination MethodSubstitution MethodGraph MethodLet's try to solve the problem now.
Let :
Amount of Bread Type 1 = A
Amount of Bread Type 2 = B
1 piece of bread type 1 requires flour as much as 150 grams and 1 piece of bread type 2 requires flour as much as 75 grams, while the total amount of flour is as much as 2250 grams, then:
[tex]150A + 75B = 2250[/tex]
[tex]2A + B = 30[/tex]
[tex]\boxed{B = 30 - 2A}[/tex] → Equation 1
1 piece of bread type 1 requires butter as much as 50 grams and 1 piece of bread type 2 requires butter as much as 75 grams, while the total amount of butter is as much as 1250 grams, then:
[tex]50A + 75B = 1250[/tex]
[tex]2A + 3B = 50[/tex]
[tex]2A + 3(30 - 2A) = 50[/tex] ← Equation 1
[tex]2A + 90 - 6A = 50[/tex]
[tex]2A - 6A = 50 - 90[/tex]
[tex]-4A = -40[/tex]
[tex]A = -40 \div -4[/tex]
[tex]\large {\boxed{A = 10}}[/tex]
[tex]B = 30 - 2A[/tex]
[tex]B = 30 - 2(10)[/tex]
[tex]B = 30 - 20[/tex]
[tex]\large {\boxed{B = 10}}[/tex]
Conclusion :The amount of Bread Type 1 is 10 pieces
The amount of Bread Type 2 is 10 pieces
Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586?Answer detailsGrade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Elimination , Substitution , Graph , Method , Linear , Equation , Simultaneous
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WILL SOMEONE HELP ME ANSWER THIS PLEASE!!!!
Luca and William are playing a video game and they have scored a total of 20,000 points. Luca scored 4,000 more points than William. If you let l= the number of points that Luca scored, and w= the number of points that William scored, then the problem can be represented by the system:
l+w=20,000 and l=w+4,000
Graph the system. How many points did each boy score?
My possible answers are:
a. William = 8,000 and Luca = 12,000
b. William = 12,000 and Luca = 8,000
d. William = 4,000 and Luca = 16,000
Answers
l+w=20000
l=w+4000
w+4000+w=20000
2w+4000=20000
2w=16000
w=8000
l = 8000 +4000 = 12000
William scored 8000, Luca scored 12000
l+w=20000, using l from above in this equation yields:
(w+4000)+w=20000 combine like terms on left side
2w+4000=20000 subtract 4000 from both sides
2w=16000 divide both sides by 2
w=8000, since l=w+4000
l=8000+4000
l=12000
William=8000 and Luca=12000