Question

Allison earns $14 an hour plus $20 an hour for every hour of overtime. Overtime hours are any hours more than 35 hours for the week. Part A: Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime.Hint: Remember to include in the equation the amount earned from working 35 hours. (3 points) Part C: Allison earned $610 in 1 week. How many hours (regular plus overtime) did she work? Show your work. (4 points)

Answer 1

Part a) Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime

Let

E-------> the amount of money earned

x------> number of hours worked

we know that

For $x\leq35$

$E=14x$

therefore

the answer part a) is

$E=14x$

Part b) Create an equation that shows the amount of wages earned, T, for working y hours of overtime

Let

T-------> the amount of money earned

y------> number of hours of overtime

we know that

$T=14*35+20y$

$T=\ 490+20y$

therefore

the answer part b) is

$T=\ 490+20y$

Part c) Allison earned $610 in 1 week. How many hours (regular plus overtime) did she work?

we know that

$35\ hours=\ 490$

$\ 610-\ 490=\ 120$

Divide $\ 120$ by  $\ 20$----> to obtain the hours of overtime

$\frac{120}{20}=6\ hours\ of\ overtime$

So

Allison works

$35+6=41\ hours$

$Regular=35\ hours\\ Overtime=6\ hours$

therefore

the answer part c) is

$Regular=35\ hours\\ Overtime=6\ hours$