Word Problem: Coins

[elancee]

I have practiced many of these problems and thought I understood how to figure them, but achieving the answer to the following escapes me (and the friends I've asked to help):

The dollar amount of coins is $296. The number of Quarters is 3 times the number of Nickels. The number of dimes is 10 less than the number of Quarters. What is the total number of each type of coin?

I began with the following equation:
Nickels=x Quarters=3x Dimes=3x-10

5(x)+25(3x)+10(3x-10)=$296

No matter how I've figured it, I do not come up with the correct answer for x.

 

[Ishuda]

Maybe it is because you have cents (the 5 is 5 cents for a nickle, etc.) on one side and dollars on the other side.

 

[soroban]

Hello, elancee!

Either you copied the probem incorrectly . . or there is a typo. A simple edit will correct the error.

The dollar amount of coins is $297.
The number of Quarters is 3 times the number of Nickels.
The number of Dimes is 10 less than the number of Quarters.
What is the total number of each type of coin?

I began with the following equation:
Nickels = x, Quarters = 3x, Dimes = 3x-10 . These are in cents.

\(\displaystyle \underbrace{5(x)+25(3x)+10(3x-10)}_{\color{blue}{\text{cents}}}\;=\; \underbrace{$297}_{\color{red}{\text{ dollars?}}}\)

Try: .\(\displaystyle 5(x) + 25(3x) + 10(3x-10) \;=\;29,\!700\)

 

[elancee]

Maybe it is because you have cents (the 5 is 5 cents for a nickle, etc.) on one side and dollars on the other side.

Eureka! That was my trouble. Thank you SO much. Seriously, I am grateful. I so could not find where I went wrong!

Nickels=270 Quarters=810 Dimes=800 Total=$296

Many blessings upon you, my friend!