SOLUTION: Jack collects the new nickels and quarters. The face value of he collection is $26.25. He has 50 more quarters than twice the number of nickels. How many nickels and how many quart

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Question 502977: Jack collects the new nickels and quarters. The face value of he collection is $26.25. He has 50 more quarters than twice the number of nickels. How many nickels and how many quarters does he have?
Answer by jrb1965(16) (Show Source):
You can put this solution on YOUR website!
So you set up equations to match the words:
N = Nickels
Q = Quarters
50 more means "add 50"
Twice means "multiply by 2"
So Q = 2N + 50
For the value, $26.25 = $0.25Q + $0.05N, since quarters are $0.25 and nickels are $0.05
Substitute the equation for Q into the value equation and solve
$26.25 = $0.25(2N + 50) + $0.05N (multiply $0.25 by 2N and 50)
$26.25 = $0.50N + $12.50 + $0.05N (subtract $12.50 from both sides)
$13.75 = $0.50N + $0.05N (combine N terms)
$13.75 = $0.55N (divide by $0.55)
25 = N
Q = 2N + 50 = 2(25) + 50 = 50 + 50 = 100
Answer -
N = 25
Q = 100