Irving the wishing well driver, has 10% as many quarters as nickels. If Irving has $5.25 in quarters and nickels, how many nickels does he have?

Question

Translate the word problem into an equation; then solve.

Answer 1

Let x = number of nickels

Then 0.10x = number of quarters

 

Value of nickels + value of quarters = 5.25

 

Since each nickel is worth $0.05, the value of the nickels is 0.05x.  Similarly, the value of the quarters is $0.25(0.10x).

 

So, 0.05x + 0.25(0.10x) = 5.25

      0.05x + 0.025x = 5.25

      0.075x = 5.25

              x = 70

 

He has 70 nickels and 7 quarters. 

 

Answer 2

Two equations, two unknowns:

 

1. Q=.1N   (10% as many quarters as nickels)
2. .25Q+.05N=5.25    (Money equation)

 

To make thinks simpler, we can multiply all of these equations by 10 and 100 to get ride of the decimals

 

1. 10Q=N
2. 25Q+5N=525

 

Now we get to solve.  We can easily use substitution, since the first equation is already solved for N

 

• N=10Q
• 25Q+5(10Q)=525
• 25Q+50Q=525
• 75Q=525
• Q=7
• N=10(7)=70

 

Therefore we have 7 quarters and 70 nickels