Marcus has a change jar that contains only nickels and pennis. He has 65 coins which add up tona total of 1.73. How many of each type of coins does he have.

Question: How many nickels and pennies when there are 65 coins that add up to a value of 1.73?

A. solution requiring no pencils, no calculators

If all coins are pennies, it would be worth 0.65, with (1.73-0.65) = 1.08 left over.

We can change a nickel for a penny for (0.05-0.01) = 0.04 (4 cents), so

number of nickels = 1.08/0.04=27

number of pennies = 65-27=38

Answer there are 38 pennies and 27 nickels

B. solution using a linear equation

Let n=number of nickels, then (65-n) = number of pennies.

Total value (cents) = 173 = 5n + (65-n) = 65+4n

Solve for n = (173-65) / 4=27 (number of nickels)

and (65-n) = 38 (number of pennies.

Answer there are 38 pennies and 27 nickels

C. solution using a system of equations

Let

n=number of nickels

p=number pennies

Total number of coins

n+p=65 ... (1)

Total value in cents

5n+p=173 ... (2)

Solve for n and p

(2) - (1)

5n-n+p-p=173-65

4n=108

n=27 (27 nickels)

p+n=65

p=65-n=65-27=38 (38 pennies)

Answer there are 38 pennies and 27 nickels