Question

Two numbers differ by 5. Seven times the smaller plus four times the larger is 108. Find the number

Answer 1

8 and 13

Explanation:

Given

Let both numbers be a and b where a > b

So:

`a- b =5` --- Their difference

`7b + 4a = 108` --- 7 of smaller and 4 of bigger

Required

Find both numbers

`a- b =5` --- (1)

`7b + 4a = 102` --- (2)

Make a the subject in (1)

`a = b + 5`

Substitute b + 5 for (a) in (2)

`7b + 4(b + 5) = 108`

Open bracket

`7b + 4b + 20 = 108`

Collect like terms

`7b + 4b = 108 - 20`

`11b = 88`

Divide both sides by 11

`b = (88)/(11)`

`b = 8`

Substitute 8 for b in
`a = b + 5`

`a = 8 + 5`

`a = 13`

Hence the two numbers are 8 and 13