SOLUTION: A collection of coins contains only nickels and dimes. The collection includes, 31 coins and has a face value of $2.65. how many nickels are included in the collection?

Question 668027: A collection of coins contains only nickels and dimes. The collection includes, 31 coins and has a face value of $2.65. how many nickels are included in the collection?

Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
Establish variables
x = nickels
y = dimes
...
x+y=31
.05x + .1y = 2.65
...
Substitute x into the equation
.05(31-y) +.1y = 2.65
1.55 - .05y + .1y = 2.65
...
Isolate y
.05y = 2.65 - 1.55
.05y = 1.1
...
Divide by .05
dimes
...
.05x + .1(31-x) = 2.65
.05x + 3.1 - .1x = 2.65
-.05x + 3.1 = 2.65
...
Isolate x
3.1-2.65 = .05x
.45 = .05x
Divide both sides by .05
nickels
...
Confirm
22 + 9 = 31
.....................
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