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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 $m$ nickels and $n$ dimes

Solution

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

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

Now the value of nickel is $5$ cents per nickel and we have $m$ nickels. So the amount of money (in cents) represented by $m$ nickels is $5m$ cents.

To find the amount of money (in cents) represented by $n$ 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 $n$ dimes. So the amount of money (in cents) represented by $n$ dimes is $10n$ cents.

Thus the amount of money (in cents) represented by $m$ nickels and $n$ dimes is $5m + 10n$ cents.

Therefore the algebraic expression of the given verbal statement is $5m + 10n$.

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