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

Nadia has 32 coins made up of nickles, dimes, and quarters. The sum of the number of nickels and the number of quarters is three times the number of dimes. If the total value of the coins is $4.60, how many of each kind does she have?

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

- Algebra -
**Reiny**, Sunday, January 13, 2013 at 5:22pm
x 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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