Answer:
- 100 grams of food A (x)
- 60 grams of food B (y)
Explanation:
According to this question, the group of laboratory rats are being fed a daily diet of:
- 125.6 units of niacin and 5,400 units of retinol
Let x represent the number of grams needed for food A.
Let y represent the number of grams needed for food B.
This means that:
Food A: Niacin = 0.86x, Retinol = 30x
Food B: Niacin = 0.66y, Retinol = 40y
Since there are 125.6 units of niacin fed to the rats in total, then;
0.86x (A) + 0.66y (B) = 125.6
Since there are 5400 units of retinol fed to the rats in total, then;
30x (A) + 40y (B) = 5400
Solving these two equations simultaneously using elimination method:
0.86x (A) + 0.66y (B) = 125.6 ........(eqn 1)
30x (A) + 40y (B) = 5400 ............ (eqn 2)
Multiply eqn 1 by 30 and eqn 2 by 0.86
30 × 0.86x + 0.66y = 125.6
0.86 × 30x + 40y = 5400
25.8x + 19.8y = 3768 ............ (eqn 3)
25.8x + 34.4y = 4644 ........... (eqn 4)
Subtract eqn 3 from eqn 4
14.6y = 876
Divide both sides by 14.6
y = 876/14.6
y = 60
Substitute value for y (60) into eqn 2
30x + 40y = 5400
30x + 40(60) = 5400
30x + 2400 = 5400
30x = 5400 - 2400
30x = 3000
x = 3000/30
x = 100
Therefore, she feeds the group of rats 100grams of food A (x) and 60 grams of food B (y).
