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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?

Respuesta :

merlynthewhizz
Let the one type of the bread be bread A
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.


johanrusli

The amount of Bread Type 1 is 10 pieces

The amount of Bread Type 2 is 10 pieces

Further explanation

Simultaneous Linear Equations can be solved using one of the following methods :

  • Elimination Method
  • Substitution Method
  • Graph Method

Let'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 more

  • Perimeter of Rectangle : https://brainly.com/question/12826246
  • Elimination Method : https://brainly.com/question/11233927
  • Sum of The Ages : https://brainly.com/question/11240586?

Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Elimination , Substitution , Graph , Method , Linear , Equation , Simultaneous

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