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A collection of quarters and nickels is worth $3.80. There are 24 coins in all. How many of each are there?
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n + q = 24, (1) (counting coins, nickels n and quarters q)
5n + 25q = 380. (2) (counting money in cents)
Express n = 24-q from (1) and substitute it into (2). You will get a single equation for q
5(24-q) + 25q = 380.
Simplify and solve it:
120 - 5q + 25q = 380,
20q = 380-120
20q = 260,
q = = 13.
Answer. 13 quarters and 24-13 = 11 nickels.
Check. 11*5 + 13*25 = 380.