Question 1058143
Let x represent the number of quarters, and let y represent the number of nickels.


The total value of the coins is then:


0.25x + 0.05y = 6.30


Since she has 12 more quarters than nickels, you know that:


x = y + 12


Substituting for x in the first equation gives


0.25(y + 12) + 0.05y = 6.30


0.25y + 3 + 0.05y = 6.30


0.30y + 3 = 6.30


0.30y = 6.30 - 3


0.30y = 3.30


y = 3.30 / 0.30


y = 11


x = y + 12 = 11 + 12 = 23


Solution: She has 23 quarters and 11 nickels.


Check:


0.25(23) + 0.05(11) = 5.75 + 0.55 = 6.30