Problem
5. The video store has a basic charge for a 3 day rental and a different charge per day late fee. Nate returned his video one day late and paid $5.50, Gina was four days late and paid $10,00 for her rental. What is the basic fee and the per day late fee the store charges?
Solution
For this case we can use the following notation:
y = 3 day payment x = per-day late fee
And we can set up these equations:
x+y = 5.50
4x +y= 10.00
From the first equation we can solve for x and we got:
x= 5.50 -y
We can replace this into the second equation and we got:
4(5.50-y) +y= 10.00
If we distribute the terms we got:
22 - 4y + y= 10.00
And solving for y we got:
22-10 = 3y
y= 4
and then we can solve for x and we got:
x= 5.50-4= 1.50
So our final solution would be x =1.5 and y= 4.00