Question

A newspaper carrier has $5.40 in change. He has six more quarters than dimes but five times as many nickles as quarters. How many coins of each type does he have?

Answer 1

Firstly, let's establish the value of each coin in cents:
- A quarter (Q) is equal to 25 cents
- A dime (D) is equal to 10 cents
- A nickel (N) is equal to 5 cents

The newspaper carrier has a total of $5.40, which is equal to 540 cents.

The problem gives us two important relations:
1. The number of quarters is six more than the number of dimes, so we can write this as Q = D + 6.
2. Also, the number of nickels is five times the number of quarters, so we can express this as N = 5Q.

We know that the total value the carrier has is the sum of values of all the nickels, dimes, and quarters:

Total Value = (N*5 cents) + (D*10 cents) + (Q*25 cents)

Substitute N and Q in the above equation:

Total Value = 5*(5Q cents) + (D*10 cents) + ((D+6)*25 cents)

Solving the equation for D we get D = 4. Replacing D in the equation Q = D + 6, we get Q = 4 + 6 = 10. And replacing Q in the equation N = 5Q, we get N = 5*10 = 50.

So, the carrier has 4 dimes, 10 quarters, and 50 nickels.

Answer 2

x= number of dimes
x+6= number of quarters
5(x+6)= number of nickels
$5.40= 540 cents

Add the number of each coin and set it equal to the total in cents.


x + (x + 6) + 5(x + 6)= $5.40
multiply 5 by parentheses; change dollar total to cents

x + (x + 6) + (5 * x) + (5 * 6)= 540

x + (x + 6) + 5x + 30= 540
combine like terms

7x + 36= 540
subtract 36 from both sides

7x= 504
divide both sides by 7

x= 72 dimes

x + 6= 78 quarters

5(x + 6)= 390 nickels


CHECK
72 + 78 + 390= 540
540= 540


ANSWER: There are 72 dimes, 78 quarters and 390 nickels.

Hope this helps! :)