Problema Solution
A cashier always starts the day with $60 in pennies, nickels, dimes and quarters. She begins with five times as many pennies as quarters, and the number of nickels and dimes are both twice the number of quarters. How many pennies does she start with?
Answer provided by our tutors
1 penny = 1 cent
1 nickle = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
let
p = the number of pennies, p>0, p is integer
n = the number of nickels, n>0, n is integer
d = the number of dimes, d>0, d is integer
q = the number of quarters, q>0, q is integer
A cashier always starts the day with $60 = 6000 cents in pennies, nickels, dimes and quarters:
p + 5n + 10d + 25q = 6000
She begins with five times as many pennies as quarters:
p = 5q
the number of nickels and dimes are both twice the number of quarters:
n = 2q
d = 2q
plug p = 5q, n = 2q and d = 2q into p + 5n + 10d + 25q = 6000:
5q +5*2q + 10*2q + 25q = 6000
by solving we find:
q = 100 quarters
click here to see the step by step solution of the equation:
p = 5*100
p = 500 pennies
A cashier always starts the day with 500 pennies.