Anewspaper 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?

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! :)