How many nickels are there if she has 20% more quarters than nickels for a total of $6?
in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

If she has N nickels then she has N+0.2N quarters=1.2N quarters. The total amount is $6.00 so:

0.05N+0.25×1.2N=6, 0.05N+0.3N=6, 0.35N=6, N=6/0.35=17.14. But this is not a whole number, so perhaps there were some dimes in the change. Suppose there were D dimes, value 0.1D, then 0.35N+0.1D=6.

Multiply through by 20: 7N+2D=120, and D=½(120-7N). Also 1.2N must be a whole number to give a whole number of quarters. N must also be even, so N must be a must be a multiple of 10. Let N=10 then there are 12 quarters and 25 dimes because D=½(120-70)=25. So we have 10 nickels, 12 quarters and 25 dimes=10×0.05+12×0.25+25×0.10=0.50+3.00+2.50=$6.00. Note that we can’t have N=20 because D would be negative so the only value for N=10. So she has 10 nickels. (She could have had some pennies in place of some of the dimes, but she has to have had 10 nickels so that the sum of nickels and quarters is 22 coins with a value of $3.50.)

by Top Rated User (616k points)

Related questions

Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,283 questions
86,801 answers
3,646 users