Word problems solved with algebra

Question

In a two-digit number, tens digit is 5 more than the units digit. The number itself is 8 times the sum of it's digits. What is the number?

Answer 1

Let ab be the 2-digit number.

a = b + 5 The tens digit is 5 more than the ones digit

a*10 + b = 8(a+b) . The actual number is 8 ties the sum of its digits.

Now, we have two equations and two unknowns. So, we can solve it!

10a + b = 8a + 8b

2a = 7b

2(b+5) = 7b

2b + 10 = 7b

10 = 5b

2 = b

Recall: a = b + 5

So: a = 2 + 5

a = 7

Therefore, the number, ab, is: 72