SOLUTION: you dump out your piggy bank and find that you have only nickels and dimes. there are a total of 50 coins and the coins add up to 3.90 how many nickles do you have ?

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Question 1157918: you dump out your piggy bank and find that you have only nickels and dimes. there are a total of 50 coins and the coins add up to 3.90 how many nickles do you have ?
Found 3 solutions by mananth, MathTherapy, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

you dump out your piggy bank and find that you have only nickels and dimes.
nickel 5 cents
dime 10 cents
there are a total of 50 coins
x+y =50
and the coins add up to $3.90
5x+10y = 390 (3.90==390 cents)
solve the equations
1.00 x + 1.00 y = 50.00


5.00 x + 10.00 y = 390.00 .............2
Eliminate y
multiply (1)by -10.00
Multiply (2) by 1.00
-10.00 x -10.00 y = -500.00
5.00 x 10.00 y = 390.00
Add the two equations
-5.00 x = -110.00
/ -5.00
x = 22.00
plug value of x in (1)
1.00 x + 1.00 y = 50.00
22.00 + 1.00 y = 50.00
1.00 y = 28.00
y = 28.00
Ans x = 22 numbers
y = 28 numbers





Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

you dump out your piggy bank and find that you have only nickels and dimes. there are a total of 50 coins and the coins add up to 3.90 how many nickles [sic] do you have ?
Let number of nickels be N

Then number of dimes = 50 - N

We then get: .05N + .1(50 - N) = 3.9

.05N + 5 - .1N = 3.9

.05N - .1N = 3.9 - 5

- .05N = - 1.1

Number of nickels, or  

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


We are to determine the number of nickels.


So start by seeing what the total value would be if all 50 coins were dimes: 50*10 = 500 cents or $5.00.


That is $1.10 too much, or 110 cents too much.


So imagine replacing dimes with nickels until you get the correct total of $3.90.


Each time you exchange a dime for a nickel, the total value decreases by 5 cents.


The number of times you need to do that to reduce the total by 110 cents is 110/5 = 22.


You replaced 22 of the dimes with nickels to get the correct total of $3.90.


ANSWER: 22 nickels.


 

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