SOLUTION: there are 22 quarters and nickels. if the total value is 2.50 ,how many nickels and quarters are there? Show the method you used to solve this problem

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Question 1063273: there are 22 quarters and nickels. if the total value is 2.50 ,how many nickels and quarters are there? Show the method you used to solve this problem
Found 2 solutions by ikleyn, Cromlix:
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
there are 22 quarters and nickels. if the total value is 2.50 ,how many nickels and quarters are there?
Show the method you used to solve this problem
~~~~~~~~~~~~~~~~~~~~~~ 

Let "n" be the number of nickels.

Then the number of quarters is (22-n).

The nickels  contribute 5n cents to the total.
The quarters contribute 25*(22-n) cents to the total.

The "value" equation is

5n + 25*(22-n) = 250 cents.

Simplify and solve for "n":

5n + 550 - 25n = 250,

-20n = 250 - 550,

-20n = - 300  --->  n = %28-300%29%2F%28-20%29 = 15.

Answer. 15 nickels and 22 - 15 = 7 quarters.

There is entire bunch of lessons on coin problems
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - More complicated coin problems
    - Solving coin problems mentally by grouping without using equations
    - Santa Claus helps solving coin problem
    - OVERVIEW of lessons on coin word problems
in this site.

Read them and become an expert in solution of coin problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Coin problems".


Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Make quarters = x
Make nickels = y
there are 22 quarters and nickels.
x + y = 22........Eq(1)
the total value is 2.50
25x + 5y = 250.....Eq(2)
..............
x + y = 22.......Eq(1)
25x + 5y = 250...Eq(2)
Multiply Eq(1) by 25
25x + 25y = 550.....Eq(1)
25x + 5y = 250......Eq(2)
Subtract Eq(2) from Eq(1)
......20y = 300
y = 15
Substitute y = 15 into Eq(1)
x + y = 22.......Eq(1)
x + 15 = 22
x = 22 - 15
x = 7
There are 7 quarters and 15 nickels.
Hope this helps :-)