Problema Solution
Eddie spills his cash register drawer on the floor. He has 742 coins which are a mixture of pennies, nickels, dimes and quarters. There are 10 times as many pennies as dimes, and half as many quarters as dimes. If he has $24.60 how many dimes are there?
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
He has 742 coins which are a mixture of pennies, nickels, dimes and quarters:
p + n + d + q = 742
n = 742 - (p + d + q)
There are 10 times as many pennies as dimes:
p = 10d
and half as many quarters as dimes:
q = (1/2)d
plug p = 10d and q = (1/2)d into n = 742 - (p + d + q):
n = 742 - (10d + d + (1/2)d)
he has $24.60 = 1460 cents
1*p + 5*n + 10d + 25q = 1460
plug p = 10d, q = (1/2)d and n = 742 - (10d + d + (1/2)d) into the last equation:
1*10d + 5*(742 - (10d + d + (1/2)d)) + 10d + 25*(1/2)d = 1460
by solving we find:
d = 90 dimes
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there are 90 dimes.