Question

Animals in an experiment are to be kept under a strict diet. Each animal should receive 50 grams of protein and 12 grams of fat. The laboratory technician is able to purchase two food​ mixes: Mix A has ​10% protein and ​8% ​fat; mix B has ​50% protein and ​5% fat. How many grams of each mix should be used to obtain the right diet for one​ animal?

Answer 1

Answer:100 grams of A mixed with 80 grams of B will provide the daily diet for a single animal.

Step-by-step explanation:

Step 1

The requirement for each animal is given as 50g of protein  and 12g of fat

let mix A  be represent as   containing  0.10A protein and 0.08A fat

and mix B be represented as containing 0.5B protein and 0.05B  fat

Therefore for Protein , we have   0.10A + 0.5B= 50----- Equation 1

And for fat , we have   0.08A + 0.05B= 12-------Equation 2

Step 2-- Solving

0.10A + 0.5B= 50----- Equation 1

0.08A + 0.05B= 12-------Equation 2

multiplying equation 1 by 10 and equation 2 by 100 we have

1A+ 5B=500-------Equation 3

8A+ 5B= 1200-------Equation 4

Subtracting equation 3 from equation 4

7A= 700

A = 700/7= 100

Puting value of A = 100 IN  EQUATION 3

1(100) + 5B= 500

5B= 500-100

B=400/5= 80

Therefore 100 grams of A mixed with 80 grams of B will provide the daily diet for a single animal.