Question 622099: A student has 54 coins in a bank. There are only quarters, nickles, and dimes in the bank. If there are twice as many dimes as quarters and three times as many nickels as quarters, how many dimes are in the bank?
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! To solve these types of problems, you need to write three equations using what you know.
First, you know that you have three types of coins and a total of 54 coins:
Q + D + N = 54 (Q=number of quarters, D=number of dimes, N=number of nickles)
Second, you know that there are twice as many dimes as quarters:
D = 2Q
Third, you know that there are three times as many nickles as quarters:
N = 3Q
Next you want to get rid of two of the variables (Q or D or N) by plugging the second and third equations into the first. Plug these equations into the first equation for D and N, and solve for Q:
Q + D + N = 54
Q + (2Q) + (3Q) = 54
6Q = 54
Q = 9
So there are 9 quarters.
To find the number of dimes, plug this value into the second equation:
D = 2Q
D = 2(9)
D = 18
So there are 18 dimes.
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