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