a parking meter contains quarters and nickels worth $5.85. there are 57 coins in all. find how many each there are.

Question

how many quarters are there ? how many nickels are there ?

Answer 1

Hi Karsyn--

 

Let's use a system of equations: first, you know that:

 

Q + N = 57, because the total number of quarters and nickels is 57.

 

You know a quarter is 25 cents and a nickel is 5 cents, so "some number of 25 cent quarters and some number of 5 cent nickels" is the value of the coins, which they tell you is $5.85. Call it 585 cents for now--much easier that way...

 

So 25Q + 5N = 585

and    Q +  N =   57, which also means that

 

                  N = 57 - Q

 

So wherever you see N, sub in 57 - Q.  So...

 

25Q + 5(57 - Q) = 585. Multiply using distribution:

 

25 Q + 285 - 5 Q = 585. Combine your Q's on one side, your numbers on the other:

 

20Q = 300. Divide by 20 to get:

 

Q = 15. So that means there are 15 quarters, which should mean there are 42 nickels.

 

To check, you need to figure out what the 2 piles of coins are worth:

 

15 quarters would be worth 375 cents, and 42 nickels would be worth 210 cents.

 

375 + 210 = 585 cents, or $5.85. Woo Hoo!

 

Hope this helps.

 

Matt in New York

Answer 2

Karsyn, I'll give you an example to follow.

 

Let's say there are 42 dimes and nickels that total $3.20.

 

If d = the number of dimes and n = the number of nickels, then d + n = 42 and .10d + .05n = 3.20

 

We can multiply both sides by 100 to get rid of the pesky decimals.  10d + 5n = 320

 

Now, we need to "solve" the first equation for either d or n.  Let's do n.  n = 42 - d

 

We plug that "value" for n into the 2nd equation.  10d + 5(42 - d) = 320

 

10d + 210 - 5d = 320

         5d + 210 = 320

                   5d = 110

                    d  = 22

 

n = 42 - d = 42 - 22 = 20

 

So, we have 22 dimes and 20 nickels.

 

Hope this helps!