Question 103649: A collection of dimes and quarters amounts to $1.80. There are 12 coins in all. How many of each coin are there? Answer by doukungfoo(195) (Show Source):
You can put this solution on YOUR website! lets call the number of dimes d
and the number of quarters q
Ok so just to be clear we have:
the number of dimes = d
the number of quarters = q
Now lets look at what we know:
Given: there are 12 coins in all
write an equation using d and q to express this fact
d + q = 12
What else do we know?
Given: a collection of dimes and quarters amounts to $1.80
and we should know that a quarter equals 0.25 cents
and a dime equal 0.10 cents
Again use d and q to write and equations to express this information
0.10d + 0.25q = 1.80
In other words:
.10 times the number of dimes plus .25 times the number of quarters equals $1.80
ok now we have a system of equations that we can use to solve for d and q
First take the equation d + q = 12 and set it equal to d
d = 12 - q
Now since we have shown that d equals 12-q lets use that in the second equation
0.10d + 0.25q = 1.80
0.10(12-q) + 0.25q = 1.80
1.2 - .1q + .25q = 1.80
1.2 + .15q = 1.80
.15q = .60
.15q/.15 = .60/.15
q = 4 Answer: there are 4 quarters in the collection
Now use this to find the number of dimes
d + q = 12
d + 4 = 12
d = 12 - 4
d = 8 Answer: there are 8 dimes in the collection
Check answers by trying them in both equations
d + q = 12
8 + 4 = 12
12 = 12
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0.10d + 0.25q = 1.80
0.10(8) + 0.25(4) = 1.80
0.80 + 1.00 = 1.80
1.80 = 1.80
