Answer
The answer is: Amy worked 13 hours and Kim worked 17 hours.
Work Step by Step
We assign the variables:
x = hours worked by Amy
y = hours worked by Kim
Step 1:
Find the equations that represent the problem.
We know that $x+y=30$ because the hours each one of them worked individually has to equal the total hours they worked combined.
If we solve for $x$, we get:
$x=30-y$ -> Eq. 1
We can get the second equation from the wording in the problem.
From "Amy and Kim earned a total of 428 dollars. Amy earns 12dollars/h and Kim earns 16dollars/h", we get
$12x+16y=428$ -> Eq. 2
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 1 into Eq. 2
$12(30-y)+16y=428$
$360-12y+16y=428$
$4y=428-360$
$4y=68$
$y=\frac{68}{4}$
$y=17$
-> Substitute the value for $y$ into Eq. 1
$x+17=30$
$x=30-17$
$x=13$
Step 3:
The answer is: Amy worked 13 hours and Kim worked 17 hours.
