Mr. Adams said that 10 more than 7 times his age is 9 years fewer than 5 times his age with the digits reversed. How old is Mr. Adams?

Answer 1

59

Answer 2

Heather, your answer does not work
10 more than 7 times 59 = 423
9 fewer than 5 times his age reversed
= 5(95) - 9 = 466

let the tens digit of his age be x
let the units digit of his age be y

his age is 10x+y
10 more than 7 times his age
= 7(10x+y) + 10

9 fewer than 5 times his age with the digits reversed
= 5(10y+x) - 9

they are equal:
7(10x+y) + 10 = 5(10y+x) - 9
70x + 7y + 10 = 50y + 5x - 9
65x - 43y = -19
65x = 43y - 19

if y = 8
65x = 43(8)-19 = 325
x = 5

so Mr Adams is 58

check:
10 more than 7 times his age = 7(58)+10 = 416
9 less than 5 times age reversed = 5(85) - 9 = 416
all is good!