SOLUTION: A purse containing $3.20 in quarters and dimes has, in all, 20 coins. Find the number of each kind of coin. (i need help!!!)

Question 105609: A purse containing $3.20 in quarters and dimes has, in all, 20 coins. Find the number of each kind of coin.
(i need help!!!)
Found 2 solutions by MathLover1, doukungfoo:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Ans.: 12 D, 8 Q
Let be the number of quarters, and be the number of dimes.
Then:

Or, we can write:
as a number of dimes
We know that sum of quarters and dimes is , so
We ca write following equation:
+* =
� =

Then,

Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
lets call the number of quarters x
and the number of dimes y
number of quarters = x
number of dimes = y
Given: there are a total of 20 coins
x + y = 20
Given: the value of all coins is $3.20
Known: a dime is worth .10 cents
and a quarter is worth .25 cents
.25x + .10y = $3.20
In other words, .25 times the number of quarters (x) plus .10 times the number of dimes (y) equals $3.20
So now we have a system of equations that we can use to solve for x and y
x + y = 20
AND
.25x + .10y = 3.20
Start with the first equation and set it equal to x
x + y = 20
x = 20 - y
Now since we have shown that x equals 20-y we can substitute the x in the second equation with 20-y and solve for y
.25x + .10y = 3.20
.25(20-y) + .10y = 3.20
5 - .25y + .10y = 3.20
5 - .15y = 3.20
-.15y = -1.80
y = 12
Answer: The purse contains 12 dimes
Now we can use this to solve for x
x + y = 20
x + 12 = 20
x = 8
Answer: The purse contains 8 quarters
Check answers by trying them in both equations
x + y = 20
8 + 12 = 20
20 = 20
-------------
.25x + .10y = 3.20
.25(8) + .10(12) = 3.20
2 + 1.20 = 3.20
3.20 = 3.20

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