Question

Allyson has 60 purple buttons, 36 black buttons, and 24 green buttons. She wants each bin to have only one color and all bins to have the same number of buttons. How many buttons can Allyson put in one bin?

She wants to put all of the buttons in bins.

Answer 1

10 buttons in each bins [ total 12 bins] of all three color of same numbers of buttons in each bins.

Explanation:

First find common factors of all the Three segments of numbers i.e. 60,36 and 24

Common factors

60 : 1,2,3,4,6,10,12,15,20,30,60

36 : 1,2,3,4,6,,12,36

24 : 1,2,3,4,6,,12,24

so common factor for 60.36.and 24 as below-

1,2,3,4,6,and 12

And Greatest common factor [GCF] is 12

So divide by all the segments by 12

`60/12=5`

`36/12=3`

`24/12`=2

so Allyson needs 12 bins to accommodate the buttons as mentioned below :-

Purple buttons 5 Nos in each bins [`5*12=60`]

Black buttons 3 Nos in each bins [`3*12=36`]

Green buttons 2 Nos in each bins [`2*12=24`]

so Total 10 Numbers of buttons [`5+3+2=10`] in 12 numbers of bins.