Question

A newspaper carrier has ​$4.40 in change. He has six more quarters than dimes but three times as many nickels as quarters. How many coins of each type does he​ have?

Answer 1

• 10 quarters, 4 dimes and 30 nickels

Explanation:

Given:

• Quarter = 25c, their number is q
• Dime = 10c, their number is d
• Nickel = 5c, their number is n
• Total amount = $4.40 = 440 c

Equations:

• q = d + 6
• n = 3q
• 25q + 10d + 5n = 440

Solve by substitution:

• n = 3q = 3(d + 6) = 3d + 18

• 25(d + 6) + 10d + 5(3d + 18) = 440
• 25d + 150 + 10d + 15d + 90 = 440
• 50d + 240 = 440
• 50d = 200
• d = 4

Find n and q:

• n = 3*4 + 18 = 30
• q = 4 + 6 = 10