Math CentralQuandaries & Queries


Question from val, a student:

I would like help working out a math word problem. A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters. Could you teach me how to find this formula?

Hi Val,

I would start by letting n be the number of nickels, d the number of dimes and q the number of quarters. You are told that the number of coins is 30 so

n + d + q = 30.

The value of the 30 coins is $5.50 but I would rater work in cents so the value of the 30 coins is 550¢. Each nickel is worth 5¢, each dime 10¢ and each quarter 25¢ so

5n + 10d + 25q = 550.

The final piece of information is that there are twice as many dimes as nickels so

d = 2n.

Substitute 2n for d in each of the first two equations. This gives you two equations in n and q. Solve them for n and q.

I hope this helps,

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