Question 105609
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
<b>Answer: The purse contains 12 dimes</B>
Now we can use this to solve for x
x + y = 20
x + 12 = 20
x = 8
<b>Answer: The purse contains 8 quarters</B>
Check answers by trying them in both equations
x + y = 20
8 + 12 = 20
20 = 20
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.25x + .10y = 3.20
.25(8) + .10(12) = 3.20
2 + 1.20 = 3.20
3.20 = 3.20