Question 120565This question is from textbook Prentice Hall Mathmatics Pre-Algebra
: Thank you in advance for helping me with this. I have been working on this problem since 3:00. The directions say to write an equation to solve the word problem. Here is the word problem...
The Jaspers collect nickels, dimes, and quarters in a jar. When they count the change in the jar, there are twice as many nickels as there are quarters. If there is $15.30 in dimes and $74.80 in all, how many quarters are there?
Thanks.
This question is from textbook Prentice Hall Mathmatics Pre-Algebra
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! The directions are a little off, because you don't need AN equation, you need THREE equations.
When you are working with word problems involving coins, or different ticket prices, or the like, you need to realize that there are two sorts of relationships that you can define. One has to do with the numbers of things, as in this problem where we are concerned with the number of quarters, dimes, and nickels. The other has to do with the value of those things, as in this case, we will want to know how much money is represented by the number of quarters for example.
Let's say there are n nickels, d dimes, and q quarters.
We don't know the total number of coins, but we do know that there are twice as many nickels as quarters, so we can at least say: 
The value of the nickels is 5n cents, because each nickel is worth 5 cents. Likewise, the value of the dimes is 10d, and the value of the quarters is 25q.
The problem states that there is $15.30 in dimes. Another way to say that is that the total worth of the dimes is 1530 cents, allowing us to write:
 , which then simplifies to  , and, voila, we now know the number of dimes.
Since there was a total of $74.80 for all the coins, there must have been $74.80 - $15.30 = $59.50 in nickels and quarters. We can also say that the value of the nickels and quarters is 5950 cents. And that lets us write:
Remember that , so anywhere we see n in the value equation, we can substitute 2q, thus:
Solving:
And we have discovered the answer: There are 170 quarters.
Check the answer:
25 * 170 = 4250
5 * 2(170) = 1700
10 * 153 = 1530
4250 + 1700 + 1530 = 7480 cents, or $74.80
Hope this helps,
John
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