Question

Hoang has worked as a nurse at Springfield General Hospital for 7 years longer than her friend Bill. Two years ago, she had been

at the hospital for twice as long. How long has each been at the hospital?

Answer 1

`Bill\to 9\ years`

`H \to 16\ years`

Explanation:

Let

`H \to Hoang`

`B \to Bill`

Currently:

`H = B + 7`

Two years ago

`H - 2 = 2 * (B -2)`

Required

H and B

We have:

`H - 2 = 2 * (B -2)`

Open bracket

`H -2 =2B - 4`

Add 2 to both sides

`H -2+2 =2B - 4+2`

`H =2B -2`

Substitute
`H = B + 7`

`B + 7 =2B -2`

Collect like terms

`2B - B =7+2`

`B = 9`

Substitute
`B = 9` in
`H = B + 7`

`H = B + 7`

`H = 9 + 7`

`H = 16`