If you have 8 yellow balloons for every 12 blue balloons, then if you have 20 balloons in total, 8 out of 20 of those balloons will be yellow. Then you can set up this ratio:
[tex]\frac{8yellow}{20total} = \frac{Xyellow}{100total}[/tex]
Then, you can use either cross multiplication or multiply the numerator and denominator by the same number to help solve for x. Personally, I prefer cross multiplication, so that's what I'll show you here:
[tex]\frac{8yellow}{20total} = \frac{Xyellow}{100total} \\ 8yellow*100total=20total*Xyellow[/tex]
Finally, solve for x:
[tex]8yellow*100total=20total*Xyellow \\ 8*100=20*x \\ 800=20x \\ 800/20=20x/20 \\ x=40yellow[/tex]
If you had 100 balloons, you will have 40 yellow balloons.
Hope this helps!!
