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.
Accepted Solution
A:
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