SOLUTION: There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels, there are 3 dimes. For every 2 dimes, there are 5 quarters. There are 500 coins in all.

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Question 1100038: There are some nickels, dimes, and quarters in a large piggy bank.
For every 2 nickels, there are 3 dimes.
For every 2 dimes, there are 5 quarters.
There are 500 coins in all.
How many nickels, dimes, and quarters are in the piggy bank?
How much are the coins in the piggy bank worth all together?

Found 3 solutions by ikleyn, richwmiller, greenestamps:
Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
.
n + d + q = 500,   (1)

2n = 3d            (2)      ("For every 2 nickels, there are 3 dimes.")

2d = 5q            (3)      ("For every 2 dimes, there are 5 quarters.")


From (2),  n = .

From (3),  q = .


Substitute  (4)  and  (5) into (1).  You will get

 + d +  = 500.

Multiply by 2 both sides:


3d + 2d + 5d = 1000  ===>  10d = 1000  ====>  d =  = 100.


Answer.  100 dimes,  150 nickels  and  250  quarters.

==============
O-o-o-p-s !

The other tutor CORRECTLY DETERMINED that the above solution is wrong.

I agree, it is WRONG !

So, below I place the corrected solution. Thanks, @richwmiller !
============== 

n + d + q = 500,   (1)

 =             (2)      ("For every 2 nickels, there are 3 dimes.")

 =             (3)      ("For every 2 dimes, there are 5 quarters.")


From (2),  n = .

From (3),  q = .


Substitute  (4)  and  (5) into (1).  You will get

 + d +  = 500.

Multiply by 6 both sides:


4d + 6d + 15d = 3000  ===>  25d = 3000  ====>  d =  = 120.


Answer.  120 dimes,   = 80 nickels  and   = 300 quarters.


Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
n+d+q=500
d=3/2n
q=5/2d
n+3/2n+5/2d=500
n+3/2n+5/2*3n/2=500
n+1.5n+3.75n=500
6.25n=500
n=500/6.25
n=80 nickels
For every 2 nickels, there are 3 dimes.
80/2=40
40*3=120 dimes
d=1.5*80=120
That works
For every 2 dimes, there are 5 quarters.
120/2=60
60*5=300
q=3.75*80=300
that works
check
80+120+300=500
ok
80*.05=$4.00 in nickels
120*.10=$12.00 in dimes
300*.25=$75.00 in quarters
75+12+4=$91.00 in coins
The other tutor says:
100 dimes, 150 nickels and 250 quarters
Lets see if that meets the conditions.
For every 2 dimes, there are 5 quarters.
100 dimes
100/2=50
50*5 =250 quarters
250 quarters
For every 2 nickels, there are 3 dimes.
150 nickels
150/2=75
75*3=225 dimes
225 dimes doesn't equal 100 dimes
Guess that doesn't work.
Oops!


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

The first tutor usually gives good answers; but this time her equations (2) and (3) are backwards.

The second tutor's answer is correct. But the work he did is complicated by his use of fractions and decimals.

Try this approach, which makes the computations much easier.

The given information relates the number of nickels to the number of dimes; and it relates the number of quarters to the number of dimes:

For every 2 nickels, there are 3 dimes.
For every 2 dimes, there are 5 quarters.

To get a problem where the numbers are easier to work with, rewrite those conditions using the same number of dimes.

One of the conditions uses 3 dimes; the other uses 2. Since the least common multiple of 3 and 2 is 6, change each condition to use 6 dimes:

For every 4 nickels, there are 6 dimes.
For every 6 dimes, there are 15 quarters.

Now you can combine those into a single statement:
For every 6 dimes, there are 4 nickels and 15 quarters.

Now think of sets of coins with each set containing 6 dimes, 4 nickels, and 15 quarters. That makes 25 coins in all. If the total number of coins is 500, then the number of these sets must be 500/25 = 20.

That means all together there are 4*20 = 80 nickels, 6*20 = 120 dimes, and 15*20 = 300 quarters.

Then the total value of the coins (in dollars) is
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