What's the fastest way to do these math problems?

xiggi
Tue, 04 Aug 2009 01:52:11 +0000

In an art class, there were just enough staplers, rulers, and glue bottles so that every 2 students had to share a stapler, every 3 had to share a ruler, and every 4 had to share a glue bottle. If the sum of the number of staplers, rulers, and glue bottles used by the class was 65, how many students were in the class?

The LCM of 3, 4, and 2 is 12, so the number of students is a multiple of 12. Seeing as 12 is too small, starting off with 36 students yields 18 staplers + 12 rulers + 9 glue bottles = 39. 48 students yields 24 + 16 + 12 = 52. 60 yields 30 + 20 + 15 = 65, so the answer is 60 students.



I think you were there, but decided to plug numbers when you can simply calculate it to the end with a simple equation:

x/2 + x/3 + x/4 = 65
6x/12 + 4x/12 + 3x/12 = 65
13x/12 = 65
13x = 1265
x= 1265/13
x=12*5

This simply looks long … you answer sheet would be a LOT simpler

6x + 4x +3x
----------- = 65 and 13x = 5.13.12
12