We want to write and solve a system of equations to see how much each person earns.
What each one earned is:
- Janet = $78
- Kate = $180
- David = $75
Let's define:
- J = number of hours that Janet worked.
- D = number of hours that David worked.
- K = number of hours that Kate worked.
The information is:
<em>"Janet worked 3 hours more than David and 7 hours less than Kate"</em>
From this we can write:
J = D + 3
J = K - 7
We know that:
- David earned $7.50 per hour.
- Janet earned $6 per hour.
- Kate earned $9 per hour.
Finally, we know that Kate earned $27 more than David an Janet combined, then we can write:
$9*K = $27 + ($7.50)*D + $6*J
Then we have a system of equations:
J = D + 3
J = K - 7
$9*K = $27 + ($7.50)*D + $6*J
We can rewrite the first and second equations to get:
D = J - 3
K = J + 7
Now we can replace these two in the other equation to get:
$9*(J + 7) = $27 + ($7.50)*(J - 3)+ $6*J
Now we can solve this for J:
$9*J + $63 = $27 + $7.50*J - $22.50 + $6*J
$9*J - $7.50*J - $6*J = $27 - $63 - $22.50
-$4.50*J = -$58.60
J = (-$58.60)/(-$4.50) = 13
This means that Janet worked for 13 hours.
And with:
K = J + 7 = 13 + 7 = 20
D = J - 3 = 13 - 3 = 10
We can see that Kate worked for 20 hours and David for 10 hours.
Then each one of them earned:
Janet = 13*$6 = $78
Kate = 20*$9 = $180
David = 10*$7.50 = $75
If you want to learn more, you can read:
brainly.com/question/9351049
