SOLUTION: Louise has a collection of nickles, dimes, and quarters worth $24.75. The number of dimes is 10 more than twice the number of nickels and the number of quarters is 25 more than the

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Question 558790: Louise has a collection of nickles, dimes, and quarters worth $24.75. The number of dimes is 10 more than twice the number of nickels and the number of quarters is 25 more than the number of dimes. How many coins of each kind does she have?
Answer by mananth(16946) About Me  (Show Source):
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Louise has a collection of nickles, dimes, and quarters worth $24.75. The number of dimes is 10 more than twice the number of nickels and the number of quarters is 25 more than the number of dimes. How many coins of each kind does she have?
Nickels ----------x
dimes -----------2x+10
quarters--------(2x+10)+25
total = 24.74 = 2475 cents
value equation
5x+10(2x+10)+25(2x++35)=2475
5x+20x+100+50x+875=2475
add like terms
75x+975=2475
75x= 2475-975
75x=1500
/75
x=20 --------- nickels
dimes = 2x+10 = > 2*20+10= 50
quarters = 50+25= 75
CHECK
(75 * 25) + (50 * 10) + (20 * 5) = 2475