Question 1066294: $4 total in dimes and quarters, and there is a total of 25 coins. How many dimes and quarters?
Found 2 solutions by swincher4391, Alan3354:
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! 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!
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! $4 total in dimes and quarters, and there is a total of 25 coins. How many dimes and quarters?
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Another method, but probably not enough to get a PHD in math:
25 dimes = $2.50
Each dime replaced by a quarter adds 15 cents.
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400 - 250 = 150 cents
150/15 = 10 replacements.
--> 10 quarters & 15 dimes
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