Answer:
18
Step-by-step 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.
