(Q7).Animals in an experiment are to be kept on a strict diet. Each animal is to receive among other things 20g of protein and 6g of fat. The laboratory technicians purchased two food mixes, A and B. Mix A has 10% protein and 6% fat. Mix B has 20% protein and 2% fat. How many grams of each mix should be used?

Let x gms of mix A and y gms of mix B are to be mixed, then

Proteins Fat
Mix A x gms x gms of 10% =
10x
100
 =
x
10
 		x gms of 6% =
x.6
100
 =
3x
50
Mix B y gms y gms of 20% =
y.20
100
 =
y
5
 		y gms of 2% =
y.2
100
 =
y
50
Total
x
10
 +
y
5
 = 20 ⇒
x+y
 = 20

x + y = .......(1)
3x
50
 +
y
50
 = 6 ⇒
x+y
 = 6

x + y = ......(2)
equation (1) × () ⇒ x + y =
equation (2)         ⇒ x +     y =
y =
⇒ y =
= gm

Substituting y = in equation (1)

we get x + 2 × = 200

⇒ x + = 200

⇒ x = 200 – = gm

∴ Quantity of mix. A = gms.

Quantity of mix. B = gms.