Question

randy earns $14.50 per hour for the first 40 hours worked in a week and $21.75 per hour for hours over 40. Last week Randy earned $667. Write and solve an equation to find that time in hours, that Randy worked over 40 hours last week.

Answer 1

4 hours

Explanation:

We know the following:

Total amount Randy earned: $667

Pay for first 40 hours: $14.50 per hour

Pay after 40 hours: $21.75 per hour

We need to find the total extra hours:
`x`

If the total number of hours worked are,
`T`, then:
`x + 40 = T`

Total pay received for the first 40 hours:
`40 * 14.50 = 580`

If out of $667, Randy earns $580 from the first 40 hours, the left over are earned by extra hours.

$667 - $580 = $87 ------- (a)

Total pay received for working after 40 hours:
`21.75x`

We know from eq (a) that total pay is 87, hence we can find the number of hours using this.

`21.75x = 87\\\\x = (87)/(21.75)\\\\x = 4`

Randy worked 4 extra hours.