Max went to the store and bought 22 apples. He bought twice as many red apples as he did green, and he bought one-third as many yellow as he did red. How many of each type of apple did he buy?

Question

anonymous · Answer

@Mashy HELP

anonymous · Answer

Solve the following for g, y and r:$${g + y + r = 22, r = 2 g, 3 y = r}$$

anonymous · Answer

{g = 6, y = 4, r = 12} where g, y and r is the number of green, yellow and red apples respectively.

poopsiedoodle · Answer

yummy, for God's sake SPIT IT OUT.

anonymous · Answer

$$r=red$$$$g=green$$$$y=yellow$$
$$r=2g$$$$y={r\over3}~~\implies~~y={2g\over3}$$so lets write the equation:$$r+y+g=22$$substitute all the values:$$2g+{2g\over3}+g=22$$find common denominators:$${6g\over3}+{2g\over3}+{3g\over3}=22$$add:$${11g\over3}=22$$multiply by the reciprocal to isolate $g$:$${\cancel{3}^1\over\cancel{11}^1}\times{\cancel{11}^1g\over\cancel{3}^1}=\cancel{22}^2\times{3\over\cancel{11}^1}$$lets write that a little cleaner:$$g=2\times3$$multiply:$$g=6$$ now plug that into $r=2g$ and $y={2g\over3}$:$$r=2(6)~~~\implies~~~r=12$$ $$y={2(6)\over3}~~~\implies~~~y={12\over3}~~~\implies~~~y=4$$now lets test it out:$$r=12$$$$g=6$$$$y=4$$$$12+4+6=22~?$$$$22=22~\checkmark$$  
and thus:$$\text{Max bought 12 red, 6 green, and 4 yellow apples.}$$

anonymous · Answer

@breja  hope that helps! :)

anonymous · Answer

@yummydum THANKS

anonymous · Answer

youre welcome!