SOLUTION: Im a 9th grade student and I usually have no problem with word problems(even algebraic ones), but there is one problem which I have difficulty with; A certain number of matches

Question 441801: Im a 9th grade student and I usually have no problem with word problems(even algebraic ones), but there is one problem which I have difficulty with;
A certain number of matches are needed to fill 24 boxes, with each box containing the same number of matches. When 4 less matches are put into each box there are enough for 28 boxes. Find the total number of matches.
I just need to form an equation and the rest can be solved by me
I tried "24(x-4) = 28x" but that didnt help!
Any help would be appreciated!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A certain number of matches are needed to fill 24 boxes, with each box containing the same number of matches. When 4 less matches are put into each box there are enough for 28 boxes. Find the total number of matches.
-----------
Let "x" be the total number of matches.
Equations:
x = 28k + 4 where k is some positive integer.
x = 24p where p = is some positive integer
---
24p = 28k+4
6p = 7k +1
7k-6p = -1
------------------
Integer solution: 6*6= 7*5 -1
----
k = 5 when p = 6
Then x = 24p = 144 matches
--
Other solutions:
k = 17 when p = 20
or
k = 35 when p = 41
or
k = 47 when p = 55
etc.
----
I used a graphing calculator to find these
solutions on the "Table" after entering
y = (7x+1)/6 in the "Y=" list. Sometimes
just knowing the solutions have to be Real,
or Integer, or Natural numbers is the key
clue to the solution. Your equation would
result in the same answers I found.
==============
Cheers,
Stan H.
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