Nutrition 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?
To find: The quantity of Food A and Food B feeds by group of rats each day.
Answer to Problem 65E
The quantity of Food A fed by rats is 200 g and Food B is 40 g.
Explanation of Solution
Given:
The one group rats feed 32 units of niacin and 22,000 units of retinol.
The niacin contains by Food A is 0.12 units and Food B is 0.20 units per gram.
The retinol contains by Food A is 100 units and Food B is 50 units per gram.
Calculation:
Let the quantity of Food A be x and quantity of Food B be y.
According to the given data, a system of equations are,
Use elimination method to find the values of x and y.
Multiply equation (1) by
That is,
Add equation (2) and (3) to eliminate y, as the coefficients of y-term in both equations are negatives of each other.
The value of x is 200.
Back - substitute 200 for x in equation (1).
Simplify the above equation.
The value of y is 40.
Thus, the quantity of Food A fed by rats is 200 g and Food B is 40 g.
Chapter 10 Solutions
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