SOLUTION: how many ways to make change for .80 cents?

Algebra.Com
Question 1132084: how many ways to make change for .80 cents?
Found 4 solutions by MathLover1, ikleyn, Alan3354, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

From what you have stated, you need to find all the ways you can combine quarters, dimes, and nickels to total cents.

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.


Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
how many ways to make change for 80 cents?
~~~~~~~~~~~~~~~~~

If you want to know in how many ways you can combine 80 cents using nickels, dimes and quarters, then the Table below gives you the answer. 

               T  A  B  L  E  


N    Quarters    Dimes    Nickels    Total (cents)

 1       0          0        16        80
 2       0          1        14        80
 3       0          2        12        80
 4       0          3        10        80
 5       0          4         8        80
 6       0          5         6        80
 7       0          6         4        80
 8       0          7         2        80
 9       0          8         0        80

10       1          0        11        80
11       1          1         9        80
12       1          2         7        80
13       1          3         5        80
14       1          4         3        80
15       1          5         1        80

16       2          0         6        80
17       2          1         4        80
18       2          2         2        80
19       2          3         0        80

20       3          0         1        80


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Another useless "math" problem.
Nothing is learned from it, except it's not .80 cents.
It's .80 dollars, or 80 cents.
=================================
In response to the comments, I doubt the student learned anything by having the problem done by others.
---
I never "bad mouth" other tutors. If they submit a wrong answer, I might solve the problem with the correct answer.
---
But, there's a lower limit to what's considered a worthwhile problem. I've seen "What is 2+2?" posted more than once and no one took it seriously. I think "making change" is only slightly more interesting.
---
But my most serious complaint is doing the problems for the students. I've gotten TY notes saying, "I just want the answer." No interest in learning anything. I think doing it for them is doing a disservice.
------------
The general public has no interest in knots, it's true. The general public is not interested in mi/hr, km/hr, or in algebra, trigonometry or calculus, either, so why mention them?
=====================
I won't deign to cavil the point further.

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


This problem, and similar ones, are NOT useless. Solving them requires logical reasoning, organized thinking, and useful math skills.

Both of the responses from other tutors assumed the problem was to use only quarters, dimes, and nickels. There is no mention in the statement of the problem about not using pennies, or half dollars. But adding pennies and/or half dollars to the problem just makes the solution more tedious; the same problem solving skills are used if we just use quarters, dimes, and nickels. So I will address the same problem.

There is no need to list out all the combinations, as one tutor did successfully and the other tutor did unsuccessfully. And if the problem were the harder problem with pennies and/or half dollars, you would not want to try to write out all the solutions.

Instead, with only quarters, dimes, and nickels, you only need to look at each possible number of quarters and determine through logical analysis and simple arithmetic how many solutions there are with each number of quarters.

For example, if you use 2 quarters, that is 50 cents; you have 30 cents more to make using dimes and nickels. You can have any number of dimes from 0 to a maximum of 3; the nickels will make up anything that remains. So with 2 quarters there are 4 solutions.

The complete solution can then look like this:

0 quarters --> 80 cents left --> 0 to 8 dimes --> 9 solutions with 0 quarters
1 quarter --> 55 cents left --> 0 to 5 dimes --> 6 solutions with 1 quarter
2 quarters --> 30 cents left --> 0 to 3 dimes --> 4 solutions with 2 quarters
3 quarters --> 5 cents left --> 0 dimes --> 1 solution with 3 quarters

Total number of solutions: 9+6+4+1 = 20
RELATED QUESTIONS

how many ways can you make change for fifty cents uisng pennies, nickels, dimes, and... (answered by jim_thompson5910)
How many ways to make 30 cents (answered by Alan3354)
Make a systematic list to solve the following problem: how many ways are there to make... (answered by richwmiller)
how many different ways can you make change of 50 cents using only dimes and... (answered by JBarnum)
how many ways to make up 48 cents using... (answered by Edwin McCravy)
Lonnie has a large supply of quarters , dimes, nickels, and pennies. In how many ways... (answered by CharlesG2,Theo)
how many ways to make change for one dollar using nickels, dimes and... (answered by Edwin McCravy,pmr2teach,richard1234)
how many ways can you change 24... (answered by richard1234)
How many ways can you make change of $.94 cents using 50 cent coin, quarters, dimes,... (answered by Alan3354)