Question

A researcher performs an experiment to test a

hypothesis that involves the nutrients niacin and retinol. She

feeds one group of laboratory rats a daily diet of precisely

32 units of niacin and 22,000 units of retinol. She uses two

types of commercial pellet foods. Food A contains 0.12 unit

of niacin and 100 units of retinol per gram. Food B contains

0.20 unit of niacin and 50 units of retinol per gram. How many

grams of each food does she feed this group of rats each day?

Short answer

We get that the researcher fed 200 grams of food A and 40 grams of food B to the rats.

Step-by-step solution

Step 1. Given information.

x = grams of food A.

y = grams of food B.

Step 2. Write down the concept.

Formulating a table as case 1 and case 2, we get,

0.12x + 0.2y = 32 …….(1)

100x + 50y = 2200 ……..(2)

Step 3. Determining the values

Solving equation by elimination method we have,

10 $\times$ (0.12 + 0.2y = 32)

2 $\times$ (2x + 4y = 440)

The equation becomes

1.2x + 2y = 320

-(4x + 2y = 880)

Solving we get,

-2.8x = -560

x = 200

Substituting in (1)

1.2 $\times$ 200 + 2y = 320

2y = 320 – 200

y = 40