Problema Solution
a student makes $8.75 purchase at the bookstore with a $20 bill. the store has no bills and gives the change in quarters and fifty-cent pieces. there are 30 coins in all. how many of each kind are there?
Answer provided by our tutors
We can state this as a system of 2 equations.
Let x = quarters and y = half-dollars (50 cent pieces)
Since they sum to 30 coins, you can write:
x + y = 30
Since he used $20 on a $8.75 purchase, he'll get $11.25 back. In terms, of cents you can also write:
25x + 50y = 1125
So you have the following SYSTEMS OF EQUATIONS
{ x + y = 30
{ 25x + 50y = 1125
Solving by substitution gives us:
x + y = 30
==> x = 30 - y
25x + 50y = 1125
==> 25(30 - y) + 50y = 1125
==> 750 - 25y + 50y = 1125
==> 25y + 750 = 1125
==> 25y = 375
==> y = 15
x + y = 30
==> x + 15 = 30
==> x = 15
Therefore, he gave 15 quarters and 15 half-dollars back.
Check:
x + y = 30
==> 15 + 15 = 30
==> 30 = 30 (True)
25x + 50y = 1125
==> 25(15) + 50(15) = 1125
==> 375 + 750 = 1125
==> 1125 = 1125 (True)
Therefore, it checks.
Hope this helps!