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 52.4 units of niacin and 35,995 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.22 unit of niacin and 170 units of retinol per gram. Food B contains 0.40 unit of niacin and 95 units of retinol per gram. How many grams of each food does she feed this group of rats each day?

Answer 1

200.0 g of A, and 21.00 g of B.

Step-by-step explanation:

Let's call the grams of food A as x and the grams of food B as y, so the units of niacin and retinol in food A are the units per gram multiplied by the mass:

Niacin: 0.22x, Retinol: 170x

And in food B:

Niacin: 0.40y, Retinol: 95y

The total unitis of niacin is 52.4 and of retinol is 35995, thus:

0.22x + 0.40y = 52.4

170x + 95y = 35995

Let's multiply the first equation by -772.7, and sum with the second one:

-170x - 309y = -40490

170x + 95y = 35995

---------------------------------------

-214y = -4495

y = 21.00 g of B

Thus,

0.22x + 0.40*21.00 = 52.4

0.22x = 44

x = 200.0 g of A