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?

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

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-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