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Posted by **Sara** on Sunday, January 13, 2013 at 5:01pm.

I can't figure out how to make this word problem into 3 equations.

- Algebra -
**Reiny**, Sunday, January 13, 2013 at 5:22pmx nickels

y dimes and

z quarters:

equation base on number of coins

x + y + z = 32 ------ #1

equation based on value of coins

5x + 10y + 25z = 460, which reduces to

x + 2y + 5z = 92 ----- #2

"The sum of the number of nickels and the number of quarters is three times the number of dimes"

----> x + z = 3y

x -3y + z = 0 ----- #3

There are your 3 equations,

if you do #1 - #3 , you get

4y = 32

y = 8

so #1 becomes

x + 8 + z = 32**x + z = 24**

#2 becomes

x + 16 + 5z = 92**x + 5z = 76**

subtract those two ...

4z = 52

z = 13

back into the 1st

x + 8 + 13 = 32

x = 11

looks like 11 nickels, 8 dimes and 13 quarters

Check:

number of coins = 11+8+13 = 32

value of coins = 5(11) + 10(8) + 25(13) = 460

is 11+13 equal to 3 times 8 ??

yes!

All is good

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