SOLUTION: Lonnie has a large supply of quarters , dimes, nickels, and pennies. In how many ways could she make change for 50 cents?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Lonnie has a large supply of quarters , dimes, nickels, and pennies. In how many ways could she make change for 50 cents?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 255053: Lonnie has a large supply of quarters , dimes, nickels, and pennies. In how many ways could she make change for 50 cents?
Found 2 solutions by CharlesG2, Theo:
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
Lonnie has a large supply of quarters , dimes, nickels, and pennies. In how many ways could she make change for 50 cents?
2Q
1Q 2D 1N
1Q 2D 5P
1Q 1D 3N
1Q 1D 2N 5P
1Q 1D 1N 10P
1Q 5N
1Q 4N 5P
1Q 3N 10P
1Q 2N 15P
1Q 1N 20P
1Q 25P
5D
4D 2N
4D 1N 5P
4D 10P
3D 4N
3D 3N 5P
3D 2N 10P
3D 1N 15P
3D 20P
2D 6N
2D 5N 5P
2D 4N 10P
2D 3N 15P
2D 2N 20P
2D 1N 25P
2D 30P
1D 8N
1D 7N 5P
1D 6N 10P
1D 5N 15P
1D 4N 20P
1D 3N 25P
1D 2N 30P
1D 1N 35P
1D 40P
10N
9N 5P
8N 10P
7N 15P
6N 20P
5N 25P
4N 30P
3N 35P
2N 40P
1N 45P
50P
48 ways

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
1 quarter = 25 cents
1 dime = 10 cents
1 nickel = 5 cents
1 penny = 1 cent

it would make sense to make a table of this working our way down from the highest denomination to the lowest denomination.

the total value of each row is equal to 50 cents. 

           quarters       dimes      nickels      pennies
              2             0          0            0 
              1             2          1            0           
              1             2          0            5           
              1             1          3            0 
              1             1          2            5
              1             1          1            10   *** example 1
              1             1          0            15
              1             0          5            0
              1             0          4            5
              1             0          3            10
              1             0          2            15
              1             0          1            20
              1             0          0            25
              0             5          0            0
              0             4          2            0
              0             4          1            5
              0             4          0            10
              0             3          4            0
              0             3          3            5   *** example 2
              0             3          2            10
              0             3          1            15
              0             3          0            20
              0             2          6            0
              0             2          5            5
              0             2          4            10
              0             2          3            15
              0             2          2            20
              0             2          1            25
              0             2          0            30
              0             1          8            0
              0             1          7            5
              0             1          6            10
              0             1          5            15
              0             1          4            20
              0             1          3            25
              0             1          2            30
              0             1          1            35
              0             1          0            40
              0             0          10           0
              0             0          9            5
              0             0          8            10
              0             0          7            15
              0             0          6            20
              0             0          5            25   *** example 3
              0             0          4            30
              0             0          3            35
              0             0          2            40
              0             0          1            45
              0             0          0            50

this counts out to be 49 possible combinations.

I couldn't figure out a formula to use so I just tabulated all the possible combinations I could think of.

The total is 49.

I believe I have them all covered.

Any combination you can think of should be in the table.

Example 1:

1 quarter 1 dime 1 nickel 10 pennies.

start with the quarter column and scan down until you see 1.
shift to the dime column and scan further down until you find 1.
shift to the nickel column and scan further down until you find 1.
shift to the penny column and you should see 10.

Example 2:

3 dimes 3 nickels 5 pennies.

start with the quarter column and scan down until you see 0.
shift to the dime column and scan further down until you find 3.
shift to the nickel column and scan further down until you find 3.
shift to the penny column ahd you should see 5.

Example 3:

5 nickels 25 pennies.

start with the quarter column and scan down until you see 0.
shift to the dime column and scan further down until you find 0.
shift to the nickel column and scan further down until you find 5.
shift to the penny column and you should see 25.