When the smaller of two consecutive integers is added to three times the larger, the result is 31. Find the integers.

Let x be the smaller number and y the larger:
As the numbers are consecutive y - x = 1 And 3y + x = 31 (3 times the large added to the smaller)
From the first equation y = x + 1 By substituting: 3(x + 1) + x = 31 3x + 3 + x = 31 4x = 28 x = 7
y = x + 1 y = 7 + 1 = 8

Answered by Trim | 2024-06-10

The two consecutive integers are 7 and 8. When the smaller integer, 7, is added to three times the larger integer, 24 (3 times 8), the total is 31. This satisfies the conditions of the problem.
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Answered by Trim | 2024-09-26