The sum of two positive integers is 7 times their difference. The product of the
same two numbers is 36 times their difference. What is the larger one of these
two numbers?
【Solution】
Suppose the difference is 1. Then the sum is 7. If we add twice the smaller number to
the difference, we will get the sum. Hence the smaller number is 3, and the larger
number is 4. Now the product is 12, which is 12 times the difference. However, it is
given that the product is 36 times the difference. Since 36 ÷ 12 = 3, the smaller
number is 3 × 3 = 9 and the larger number is 3 × 4 = 12.
ANS: 12