SOLUTION: A box contains $7.25 in nickels,dimes and quarters. There are 43 coins and the number of quarters is 1 more than three times the number of nickels. Find the number of quarters in t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A box contains $7.25 in nickels,dimes and quarters. There are 43 coins and the number of quarters is 1 more than three times the number of nickels. Find the number of quarters in t      Log On


   

Question 983212: A box contains $7.25 in nickels,dimes and quarters. There are 43 coins and the number of quarters is 1 more than three times the number of nickels. Find the number of quarters in the box
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
p n d q for the counts of each coin

0.01p%2B0.05n%2B0.1d%2B0.25q=7.25
p%2B5n%2B10d%2B25q=725
Note that if no pennies, but only nickels, dimes, and quarters, then
5n%2B10d%2B25q=725
n%2B2d%2B5q=145

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p%2Bn%2Bd%2Bq=43
Note that if only nickels, dimes, quarters, then NO pennies.
n%2Bd%2Bq=43
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q=1%2B3n, part of the description. Substitute into the other two simplified equations to eliminate this one variable, q.

system%28n%2B2d%2B5%283n%2B1%29=145%2Cn%2Bd%2B3n%2B1=43%29

system%28n%2B2d%2B15n%2B5=145%2C4n%2Bd%2B1=43%29

system%2816n%2B2d=140%2C4n%2Bd=42%29

system%288n%2Bd=70%2C4n%2Bd=42%29
Use Elimination Method as far as finding either n or d; quicker to eliminate d.
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4n=28
highlight%28n=7%29-----------------Getting the other two should be no trouble.