Question

Technological advances in farming made it possible to increase the crop of potatoes from 1 acre by 4 tons. As a result, from a field of 320 acres 640 tons of potatoes more were collected than before from a field of 400 acres. How many tons of potatoes were collected before the new methods and how many after the introduction of the new technology?

Answer 1

Answer:

• 320 acre field: 2560 tons before; 3840 tons after
• 400 acre field: 3200 tons before; 4800 tons after

Step-by-step explanation:

Let x represent the number of tons per acre harvested before new technology. The problem statement gives us the relation ...

  320(x +4) = 400x +640

  320x + 1280 = 400x + 640 . . . . eliminate parentheses

  640 = 80x . . . . . . . . . . . . . . . . . . add -320x-640

  8 = x . . . . . . . . . . . . . . . . . . . . . . . divide by the coefficient of x

Before new technology, 8 tons per acre were collected; afterward, 12 tons per acre were collected.

_____

The field yield was 8 tons per acre before new technology:

  320 acres × 8 tons/acre = 2560 tons

  400 acres × 8 tons/acre = 3200 tons

After new technology, the harvest was ...

  320 acres × 12 tons/acre = 3840 tons

  400 acres × 12 tons/acre = 4800 tons

The highlighted numbers are the ones being compared, so must differ by 640.