Question

Write the following as an algebraic expression. Then simplify.

The total amount of money​ (in cents) in x nickles​, (x+3) quarters​, and 3x dimes. ​(Hint: The value of a nickel is 5 ​cents, the value of a quarter is 25 ​cents, and the value of a dime is 10 ​cents.)

The total amount of money is ___ cents.
​(Simplify your answer. Do not​ factor.)

Answer 1

`60x+75`

Explanation:

We want to find the total amount of money (in cents) of the expression:

`\text{$x$ nickels, $(x+3)$ quarters, and $3x$ dimes}`

Since each nickel is worth five cents, each quarter 25 cents, and each dime ten cents, we can write that:

`\displaystyle \text{Total}=5(x)+25(x+3)+10(3x)`

Simplify. Distribute:

`T=5x+25x+75+30x`

Combine like terms. Therefore, the total amount of money (in cents) is represented by:

`T=60x+75`