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Question

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 mm dimes and nn quarters

Solution

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

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

Now the value of dime is 1010 cents per dime and we have mm dimes. So the amount of money (in cents) represented by mm dimes is 10m10m cents.

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

Now the value of nickel is 2525 cents per quarter and we have nn quarters. So the amount of money (in cents) represented by nn quarters is 25n25n cents.

Thus the amount of money (in cents) represented by mm dimes and nn quarters is 10m+25n10m + 25n cents.

Therefore the algebraic expression of the given verbal statement is 10m+25n10m + 25n.

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