SOLUTION: Suppose tom has 23 coins totaling 3.80. If he has only dimes and quarters, how many of each type does he have

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Question 823458: Suppose tom has 23 coins totaling 3.80. If he has only dimes and quarters, how many of each type does he have
Answer by richwmiller(17219) About Me  (Show Source):
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at least three are dimes
so we have 20 coins with a total of 3.50
if the rest are all quarters then there would be 4*3+2=14 but we need 20
so we are 6 short
we must have dimes in multiples of 5
12 q + 5 d=3.50 but only 17 coins
10q +10 dimes=3.50 with 20 coins
10 q +13 dimes total
algebraic solution
d+q=23
25q+10d=380
d=23-q
25q+10*(23-q)=380
25q+230-10q=380
15q=150
q=10
d=13