A jar of dimes an quarters is worth $4.55. If there are the same number of dimes as quarters,what is the value of only the dimes?
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This is an algebra problem. The problem can be expressed as a system of equations. First, assume that we have d dimes and q quarters. Then the total amount of money in the jar is: \[0.1\times d + 0.25\times q\] For example, 1 dime and 2 quarters would be \[0.1\times1+0.25\times2=0.6\] That is 0.6 dollars, so 60 cents. The second fact we have is that we have the same number of each, so this gives the system of equations:
\[0.1d +0.25q=4.55\] \[d=q\]
Since we know d=q, substitute this in to the first equation to get:\[0.1q+0.25q=4.55\]Now solve for q to get:\[0.35q=4.55\rightarrow q=4.55\div0.35=13\]
So you have 13 quarters, which means you have 13 dimes. Check your answer by plugging d=13 and q=13 in to the original equation.