SOLUTION: jeremy pays for lunch using 75 coins consisting of quaters and nickels . if the total for his lunch is 13.55, find the number of quaters and nickels

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Question 162061: jeremy pays for lunch using 75 coins consisting of quaters and nickels . if the total for his lunch is 13.55, find the number of quaters and nickels
Answer by schrammbledeggs(41) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of quarters
Let y = number of nickels


From the first sentence we can get the equation:
x + y = 75

From the second sentence we can get the equation:
0.25x + 0.05y = 13.55


We can use substitution to find our answer...let's first solve for number of quarters...

We start by solving the first equation for y so we can solve the second equation for x...

x + y = 75
x + y - x = 75 - x
y = 75 - x

Plug that value of y into the 2nd equation:

0.25x + 0.05 (75 - x) = 13.55
0.25x + 3.75 - 0.05x = 13.55
0.20x + 3.75 = 13.55
0.20x + 3.75 - 3.75 = 13.55 - 3.75
0.20x = 9.80
x = 9.80 / 0.20
x = 49 quarters

Now we can plug our x-value into our original equation:

x + y = 75
49 + y = 75
49 + y - 49 = 75 - 49
y = 26 nickels

So Jeremy paid for lunch with 49 quarters and 26 nickels.
:)