Question 833832: Please help me write an equation for this word problem: Pasha has a box with 40 coins consisting of dimes, quarters, and nickels that are worth $5.25. There are 5 more nickels than quarters. How many of each coin does she have? So far I've got this down on my paper: d+q+n=40 and 10d+25q+5(q+5)=525.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Pasha has a box with 40 coins consisting of dimes, quarters, and nickels that are worth $5.25.
There are 5 more nickels than quarters.
How many of each coin does she have?
So far I've got this down on my paper: d+q+n=40 and 10d+25q+5(q+5)=525.
:
Replace n with (q+5) in the 1st equation also
d + q + (q+5) = 40
Combine like terms, subtract 5 from each side and you have
d + 2q = 35
d = (35-2q); we can use the form for substitution
:
10d+25q+5(q+5)=525.
multiply what's inside the brackets
10d + 25q + 5q + 25 = 525
Combine like terms, subtract 25 from both sides and you have
10d + 30q = 500
substitute (35-2q) for d
10(35-2q) + 30q = 500
350 - 20q + 30q = 500
10q = 500 - 350
10q = 150
q = 150/10
q = 15 quarters
then find n
n = 15 + 5
n = 20 nickels
find d
d + 15 + 20 = 40
d = 40 - 35
d = 5 dimes
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:
Check this
5(20) + 10(5) + 25(15) =
100 + 50 + 375 = 525
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