Question

In a two-digit number the units’ digit is 7 more than the tens’ digit. The number with digits reversed is three times as large as the sum of the original number and the two digits. Find the number.

Answer 1

18

Explanation:

Answer 2

18

Explanation:

Let t and u represent the tens digit and the units digit, respectively. The problem statement lets us write equations relating these variables.

u = t + 7 . . . . the units digit is 7 more than the tens digit

10u +t = 3(10t +u +t +u) . . . . the number with digits reversed is 3 times ...

The second equation can be simplified to ...

10u +t = 33t +6u . . . . eliminate parentheses

4u = 32t . . . . . add -6u-t

u = 8t . . . . . . . . divide by 4

Equating the two expressions for u, we have

t +7 = 8t

7 = 7t . . . . subtract t

1 = t . . . . . divide by 7

u = 8t = 8 . . . . find the value of u

(t, u) = (1, 8)

The two-digit number is 18.