Olivia has 40 coins made up of quarters and dimes. altogether they make $7.00. how many quarters does she have? how many dimes does she have?

Let Q be quarters and D be dimes.
We can make two equations out of the given information
Q+D=40
0.25Q+0.1D=7
we can manipulate the second equation to be:
2.5Q+D=70(by multiplying everything by 10)
Now we subtract the first equation from this to get:
2.5Q-Q+D-D=70-40 or 1.5Q=30
Thus Q equals 20.
Since Q+D=40, 20+D=40 so D=20
Thus there are 20 Dimes, and 20 Quarters

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