Question bank / Linear equations in two variables

Math · AlgebraHard

A gardener applies xx pounds of fertilizer A, which is 20%20\% nitrogen by weight, and yy pounds of fertilizer B, which is 32%32\% nitrogen by weight. The equation 0.20x+0.32y=160.20x + 0.32y = 16 represents the combinations that supply exactly 1616 pounds of nitrogen. If the gardener increases the amount of fertilizer B by 55 pounds, how must the amount of fertilizer A change so that the total nitrogen is still 1616 pounds?

A

Decrease by 1.61.6 pounds

B

Decrease by 3.1253.125 pounds

C

Decrease by 88 pounds

D

Increase by 88 pounds

Show answer and explanation

Answer: C

Adding 55 pounds of fertilizer B adds 0.32(5)=1.60.32(5) = 1.6 pounds of nitrogen. To keep the total at 1616 pounds, fertilizer A must supply 1.61.6 fewer pounds of nitrogen. Each pound of fertilizer A supplies 0.200.20 pound of nitrogen, so the amount of A must decrease by 1.60.20=8\frac{1.6}{0.20} = 8 pounds.

Choice A is the change in the amount of nitrogen, not the change in the amount of fertilizer A.

Why the other choices are wrong

  • A. 1.6 pounds is the extra nitrogen from fertilizer B. Fertilizer A must drop by 1.6 ÷ 0.20 = 8 pounds to remove that much nitrogen.
  • B. This computes 0.20 × 5 ÷ 0.32, which swaps the two percentages.
  • D. Adding fertilizer B raises the nitrogen, so the amount of fertilizer A has to go down, not up.
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