There were some green and red apples in a box. Ted took up 2/11 of the green apples from the box. He replaced each of these green apples taken out with red apples. After that, he took out 2/5 of the green apples and 1/3 of the red apples. There were 108 green apples and 228 red apples left in the box in the end. What was the total number of green and red apples in the box at first?
+128460 Let the original number of red apples = R and the original number of green apples = G
We have that
R + (2/11) G - (1/3)[ R + (2/11)G ] = 228
G - (2/11)G - (2/5) [ G -(2/11)G ] =108
Looking at the second equation and simplifying we have
(9/11)G - ( 2/5)G + (4/55) G = 108
( 45/55)G - (22/55)G + ( 4/55)G =108
(27/55) G =108
G = 108 / 27 * 55 = 220 = original number of green apples
And simplifying the first equation we have
R + (2/11)(220) - ( 1/3) [ R + (2/11)(220)] = 228
R + 40 - (1/3)R - (1/3) (40) = 228
(2/3)R + 40 - 40/3 = 228
2R + 120 - 40 = 684
2R + 80 = 684
2R = 604
R = 604 / 2 = 302 = original number of red apples
R + G = 302 + 228 = 530
