Algebra
posted by Sara .
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.

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
Respond to this Question
Similar Questions

math
rose counted her money and found that her 25 coins which were nickels, dimes, and quarters were worth $3.20. The number of dimes exceeded the number of nickels by 4. How many coins of each kind did she have? 
pre calc
rose counted her money and found that her 25 coins which were nickels, dimes, and quarters were worth $3.20. The number of dimes exceeded the number of nickels by 4. How many coins of each kind did she have? 
Algebra
Alycia's pggy bank has dimes and quarters in it. The numbers of dimes is four less than three times the number of quarters. If the total value of the coins is $7.85, how many dimes are in the piggy bank? 
Algebra
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? 
Algebra
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? 
Algebra
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? 
Algebra
A coin collection contains 30 coins in nickels, dimes, and quarters. There are three more dimes than nickels. The value of the coins is 3.55. Find the number of quarters in the collection. 
Intermediate algebra
A collection of nickels dimes and quarters consists of 50 coins with a total of $5.50. If there are two times as many dimes as quarters find the number of each type of coins? 
algebra
A box contains $7.80 in nickels, dimes, and quarters. There are 46 coins in all, and the sum of the numbers of nickels and dimes is 2 less than the number of quarters. How many coins of each kind are there? 
College Algebra
A box contains $7.80 in nickels, dimes, and quarters. There are 46 coins in all, and the sum of the numbers of nickels and dimes is 2 less than the number of quarters. How many coins of each kind are there?