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# Write an algebraic expression that represents the specified quantity in the verbal statement, and simplify if possible. The amount of money (in cents) represented by $m$ dimes and $n$ quarters

Solution

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Given verbal statement is `the amount of money (in cents) represented by $m$ dimes and $n$ quarters'.

To find the amount of money (in cents) represented by $m$ dimes, we have to multiply the value of a dime in cents with number of dimes.

Now the value of dime is $10$ cents per dime and we have $m$ dimes. So the amount of money (in cents) represented by $m$ dimes is $10m$ cents.

To find the amount of money (in cents) represented by $n$ quarters, we have to multiply the value of a quarter in cents with number of quarter.

Now the value of nickel is $25$ cents per quarter and we have $n$ quarters. So the amount of money (in cents) represented by $n$ quarters is $25n$ cents.

Thus the amount of money (in cents) represented by $m$ dimes and $n$ quarters is $10m + 25n$ cents.

Therefore the algebraic expression of the given verbal statement is $10m + 25n$.

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