SOLUTION: A student makes a $10.50 purchase at the bookstore with a $20.00 dollar bill. The store has no bills and gives change in quaters and fifty-cent pieces. There are 30 coins in all, h
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Question 320204: A student makes a $10.50 purchase at the bookstore with a $20.00 dollar bill. The store has no bills and gives change in quaters and fifty-cent pieces. There are 30 coins in all, how many of each are there? Found 3 solutions by solver91311, Sunny Day, josmiceli:Answer by solver91311(24713) (Show Source):
Let represent the number of quarters. Then, since there are 30 coins in all, there must be 50-cent pieces. The purchase was $10.50, so the change from $20.00 must be $9.50 or 950 cents.
Quarters are worth 25 cents, so quarters must be worth cents. Likewise, 50-cent pieces are worth...wait for it now...50 cents, so 50-cent pieces must be worth cents.
You can put this solution on YOUR website! Let 'x' be the number of quarters.
Then the balance he got in quarters = 0.25x
Then the number of fifty cent coins = 30 - x. (since he was given a total of 30 coins).
The balance in fifty cents = 0.5(30 - x) = 0.5X30 - 0.5x = 15 - 0.5x
The balance he got = 20 - 10.5 = $ 9.5
i.e. 0.25x + (15 - 0.5x) = $ 9.5 [balance in quarters and fifty cents together]
0.25x - 0.5x + 15 = 9.5
-0.25x = 9.5 - 15
-0.25x = -5.5
i.e. 0.25x = 5.5
x = 5.5/0.25 = 22
So there are 22 quarters and (30 -22) = 8 fifty cent coins.
You can put this solution on YOUR website! The change is $9.50. fifty-cent pieces adds up to dollars fifty-cent pieces adds up to dollars, and
if the rest is quarters, that is , and that's too much
-------------------------------- fifty-cent pieces adds up to dollars
and dollars and That's cents over
-------------------------------- fifty cent pieces adds up to dollars
and dollars That's cents over
-------------------------------- fifty cent pieces = dollars dollars and this is the answer
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The change is 8 fifty-cent piece and 22 quarters
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