SOLUTION: Sonia has a bag of coins with only nickels and quarters. She has 105 coins that add up to $17.25. How many nickels and quarters does she have?

Question 230461: Sonia has a bag of coins with only nickels and quarters. She has 105 coins that add up to $17.25. How many nickels and quarters does she have?
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Let n be the number of nickles and q be the number of quarters. Then from the problem above we get the system of equations:

n+q = 105
0.05n+0.25q = 17.25

Just because I hate working with decimals I'm going to multiply the second equation by 100 to get rid of the decimals.

5n + 25q = 1725

Now we can solve the system by using the substitution method. First solve the first equation for n.

n = 105-q.

Now substitute that equation into the second equation and solve for q. I will leave you to do the algebra but you should get that q = 60. Now substitute that back into the equation we found for n and you should find that n = 45.

So Sonia has 60 quarters and 45 nickles.
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