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 41.59 units of niacin and 17,995 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.22 unit of niacin and 100 units of retinol per gram. Food B contains 0.23 unit of niacin and 65 units of retinol per gram. How many grams of each food does she feed this group of rats each day

Answer 1

Food A = 165 grams

Food B = 23 grams

Explanation:

Daily precise diet fed to the group:

Niacin = 41.59 units

Retinol = 17,995 units

Two food types :

Food A :

Niacin = 0.22 units per gram

Retinol = 100 units per gram

Food B:

Niacin = 0.23 units per gram

Retinol = 65 units per gram

Let:

a = gram of food A fed per day

b = gram of food B fed per day

Hence in 'a' grams of food A:

0.22a of Niacin + 100a of Retinol

In 'b' grams of food B:

0.23b of Niacin + 65b of retinol

Recall :

Total Niacin = 41.59 ; total Retinol = 17995

Then,

0.22a + 0.23b = 41.59 - - - (1)

100a + 65b = 17995 - - - (2)

From (2) ; 100a + 65b = 17995

100a = 17995 - 65b

a = 179.95 - 0.65b - - - (3)

Substitute (3) into (1)

0.22(179.95 - 0.65b) + 0.23b = 41.59

39.589 - 0.143b + 0.23b = 41.59

0.087b = 2.001

b = 2.001 / 0.087

b = 23

Put b = 23 in (3)

a = 179.95 - 0.65(23)

a = 179.95 - 14.95

a = 165