berts says that 10 more than 7 times his age is 9 years fewer than 5 times hs age with the digits reversed. How old is bert

Question

berts says that 10 more than 7 times his age is 9 years fewer than 5 times hs age with the digits reversed. How old is bert

Answer 1

Bert's age=ab which means 10a+b

Bert's age with the digits reversed=ba which means 10b+a

7(10a+b)+10=5(10b+a)-9

70a+7b+10=50b+5a-9

70a-5a+7b-50b=-9-10

65a-43b=-19

using trial and error...  (to find a number divisible by 43)

a=1, 2, 3, 4, 5

a=5

65*5-43b=-19

325-43b=-19

325+19=43b

344=43b

b=344/43

b=8

Bert is 58

7*58+10=5*85-9

406+10=425-9

416=416