math word problem

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mashra mashra
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math word problem

There are 49 pennies, nickels, and quarters in a drawer. If their combined value is $2.41, and the number of
pennies exceeds the number of nickels by 8, how many of each type are there?
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Re: math word problem

x = number of nickels
x + 8 = number of pennies  
49 - (2x + 8) = number of quarters   ← 49 total coins in drawer

0.05x + 0.01(x + 8) + 0.25(41 - 2x) = 2.41   ← value of coin times number of coins equals total value
0.05x + 0.01x + 0.08 + 10.25 - 0.5x = 2.41   ← distributive property
-0.44x + 10.33 = 2.41   ← combined
-0.44x = -7.92   ← subtracted 10.33
x = 18   ← divided by -0.44
x + 8 = 26   ← substituted
49 - (2x + 8) = 5   ← substituted

18 nickels
26 pennies
5 quarters

- Proof