SOLUTION: Sandy has a total of 41 quarters and nickels. The value of her money is $7.05. How many of each coin does she have?

Question 451513: Sandy has a total of 41 quarters and nickels. The value of her money is $7.05. How many of each coin does she have?
Answer by pedjajov(51) (Show Source): You can put this solution on YOUR website!
Let's mark:
q - number of quarters Sandy has
n - number of nickels Sandy has
Number of coins Sandy has is
q + n = 41
Everything has to be in the same units so $7.05 = 705 cents
Value of coins Sandy has is
25*q + 5*n = 705
We have two equations with two variables
q + n = 41, let express q as q = 41 - n
25*q + 5*n = 705
25*(41-n) + 5*n = 705 , replace q with expression from above
1025 - 25*n + 5*n = 705 , multiply
1025 - 705 = 25*n - 5*n , move unknowns to one and numbers to other side
320 = 20*n , combine variables and numbers on each side
n = 320/20 , invert multiplication
n = 16, number of nickles Sandy has
q = 41 - 16 , replace n witht he found value
q = 25, number of quarters Sandy has
check: 25*25 + 5*16 = 625 + 80 = 705, OK
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