Math CentralQuandaries & Queries


Question from Sonia, a student:

Use an algebraic approach to solve the problem. Abby has 45 coins, consisting only of dimes and quarters, worth $6.6. How many dimes and how many quarters does she have?

I don't just want to know the answer to the word problem. I want to know how to set it up. I really think that's my only problem i don't know how to write it out algebraically.


We have two responses for you


There are two properties of the coins that are important. The first is the number of coins that Abby has and the second is the value of the coins. There are dimes and quarters so let D be the number of dimes she has and Q be the number of Quarters she has. Thus she has D + Q coins in total. What is the value of her coins in dollars?

Each dime is worth 10 cents or a tenth of a dollar so her dimes are worth $0.10D. What is the value of her quarters? What is the value of all of her coins?

I hope this helps. If you need further assistance write back,



Let's suppose a person has some 5 cent coins and some 10 cent coins, with a total of 27 coins in all.
Suppose the total amount of money in hand is $1.55. Let's figure out how many coins of each type
there are.

There are several pieces of information.
* there are 27 coins
* each coin is worth 5 cents or 10 cents
* the total amount of money is $1.55

The way to set up problems like this is to find ways to calculate the values that you are given in terms
of the values you need to find out. You want to find out the number of 5 cent coins and the number of
10 cent coins.

The amount of money on hand is 5 x (number of 5 cent coins) + 10 x (number of 10 cent coins).
Therefore $1.55 = 5 x (number of 5 cent coins) + 10 x (number of 10 cent coins). The left hand side of
this equation is in dollars and the right hand side is in cents. We need both sides to be expressed in
a common unit. Since one dollar is 100 cents, $1.55 = 155 cents. Now the equation is
155 = 5 x (number of 5 cent coins) + 10 x (number of 10 cent coins).

The total number of coins is (number of 5 cent coins) + (number of 10 cent coins).
Therefore 27 = 5 x (number of 5 cent coins) + 10 x (number of 10 cent coins).

If we use n as shorthand for (number of 5 cent coins), and d as shorthand for (number of 10 cent coins),
then what we did above becomes

5n + 10d = 155
n + d = 27

The solution is d = 4 and n = 23.

Good luck!

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