i have 40 coins. All of them are nickels, dimes or quarters. The total was 5.55. If i have three less quarters than dimes, how many quarters do i have
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 d is the number of dimes, then there are d-3 quarters, so 5.55=0.05n+0.1d+0.25(d-3), where n=number of nickels. So 5.55=0.05n+0.35d-0.75; and n+d+d-3=40. Therefore 0.05n+0.35d=6.30 and n+2d=43. Multiply the first equation by 100: 5n+35d=630; 5(43-2d)+35d=630 substituting for n; 215-10d+35d=630. 25d=415, so d=415/25=83/5=16.6, which is not a whole number. If we take d=16, then this is $1.60, and 13*0.25=$3.25, making $4.85 with 29 coins. This is a shortfall of $0.70 which is 14 nickels, making 43 coins altogether, not 40. 

If the question should have read "3 times less quarters than dimes": 5.55=0.05n+0.1d+0.25d/3 and n+4d/3=40. So 16.65=0.15n+0.3d+0.25d and 3n+4d=120; 16.65=0.15n+0.55d; 1665=15n+55d=15(120-4d)/3+55d; 4995=1800-60d+165d; 105d=3195 and d=30.43, which is not much better than the first solution! There would be 30 dimes ($3), 10 quarters ($2.50) and 1 nickel ($0.05), a total of 41 coins.


by Top Rated User (1.0m points)

Related questions

Welcome to MathHomeworkAnswers.org, 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!
87,021 questions
96,296 answers
24,339 users