SOLUTION: A total of M matches is needed to fill 30 match boxes with the same number of matches in each box. (a) How many matches are in each box? (b) If each box has three match sticks

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A total of M matches is needed to fill 30 match boxes with the same number of matches in each box. (a) How many matches are in each box? (b) If each box has three match sticks       Log On


   

Question 1112234: A total of M matches is needed to fill 30 match boxes with the same number of matches in each box.
(a) How many matches are in each box?
(b) If each box has three match sticks fewer, there would be enough sticks for 32 boxes,what is the value of m?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
+M%2F30+ = the number of matches in each box
(b)
+M%2F30+-+3+ = number of matches/box with
three fewer per box
----------------------------
[ matches/box ] x [ number of boxes ] = [ total number of matches ]
+%28+M%2F30+-+3+%29%2A32+=+M+
+M%2A%28+32%2F30+%29+-+3%2A32+=+M+
Multiply both sides by +30+
+32M+-+96%2A30+=+30M+
+2M+=+2880+
+M+=+1440+
-------------------------
check answer:
+%28+M%2F30+-+3+%29%2A32+=+M+
+%28+1440%2F30+-+3+%29%2A32+=+1440+%7C
+%28+48+-+3+%29%2A32+=+1440+
+45%2A32+=+1440+
+1440+=+1440+
OK