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newspaper carrier has 4.45 in change. he has five more quarters than dimes but four times as many nickles as quarters. how many coins of each type does he have

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Michael B. | Math Teacher and Lead Curriculum Writer for Math TutoringMath Teacher and Lead Curriculum Writer ...
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One way to approach this type of question is to write a system of equations.
Establish variables:
q=number of quarters
d=number of dimes
n=number of nickels
p=number of pennies
Create equations based on your information:
Use the value of each coin times the number of that coin to build the equation for your total value.
0.25q + 0.10d + 0.05n + 0.01p = [your $ value here]
Then write your comparison equations.
[for example]
If I had 6 times as many pennies as dimes...
p = 6*d
If I had 3 more nickels than quarters...
n = q + 3
Depending on which course you're taking and where you're at, you can either substitute your smaller equations into the longer equation until you isolate one variable (then solve for the others), or create an augmented matrix and row-reduce.
*In your case, notice that everything comes back to quarters. That might be your biggest clue to what variable you should hunt down first! Good luck!