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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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?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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.
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