Question

Hector received a pay raise this year. The raise was 6% of last year's salary. This year he will earn $15,900. What was his salary last year before the raise?

Answer 1

See a solution process below:

Explanation:

The formula for calculating a new salary is:

`n = p + (p * r)` Where:

`n` is the new salary: $15,900 for this problem.

`p` is the previous salary: what we are solving for in this problem.

`r` is the pay raise percentage: 6% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 6% can be written as `6/100`.

Substituting and solving for `p` gives:

`$15900 = p + (p * 6/100)`

`$15900 = p + (6p)/100`

`$15900 = 100/100p + 6/100p`

`$15900 = (100/100 + 6/100)p`

`$15900 = 106/100p`

`color(red)(100)/color(blue)(106) xx $15900 = color(red)(100)/color(blue)(106) xx 106/100p`

`($1590000)/color(blue)(106) = cancel(color(red)(100))/cancel(color(blue)(106)) xx color(blue)(cancel(color(black)(106)))/color(red)(cancel(color(black)(100)))p`

`$15000 = p`

`p = $15000`

Hector's salary last year before the raise was: `color(red)($15,000)`