Question 1066294
Let d be the number of dimes.  Let q be the number of quarters.

"there is a total of 25 coins" means that if you added up the number of dimes and quarters you would get 25. How can we represent this using our variables?

d+q = 25

Easy enough. But what do we do now? We're also told that we have "$4 in total". Well, if you had 10 quarters, how much money would you have? How can you figure it out? You would take 10 * .25 and get $2.50. 

So what if I have "q" quarters? Well then I have .25q in change.  So how can I represent the total amount of money by having "d" dimes and "q" quarters?

.10d + .25q = 4.00

And there we have it, we have set up a system of equations and now we can just use our favorite method to solve. Personally, I like elimination, but if you prefer substitution send me an email and I'll work it out that way. swincher4391@yahoo.com

So we have:

d+q = 25
.10d + .25q = 4.00

I'll choose a variable to eliminate. I could multiply the 2nd equation by 10 and then subtract to get rid of "d", but that would make us deal with negatives (which we could do, but I try to avoid), so let's eliminate q by multiplying the 2nd equation by 4 and then subtracting.

d + q = 25

4(.10d + .25q = 4.00)

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d + q = 25

.4d + q = 16

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.6d = 9

d = 9/.6 = 15

Now if at the very beginning I told you I had 25 quarters and dimes and 15 of them are dimes... how many quarters do we have? You'd think that was a pretty simple problem.   In other words:     15 + q = 25.    

q = 10.

We have 15 dimes and 10 quarters.

It's always good to check though.


15 * .1 = 1.50

10 * .25 = 2.50
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$4.00!