Ethan had some red beans and green beans. The ratio of the number of red beans to the number of green beans was 5: 8. After Fandi took away 4 red beans and 4 green beans, the new ratio became 1: 2. Find the total number of beans he had at the end.

Answer 1

Let the number of red beans initially be 5x, and the number of green beans be 8x.
After Fandi took away 4 red beans and 4 green beans, the number of red beans became 5x - 4, and the number of green beans became 8x - 4.
After Fandi took away 4 red beans and 4 green beans, the ratio of the number of red beans to the number of green beans became (5x - 4): (8x - 4) = 1/2.
2(5x - 4) = 1(8x - 4).
10x - 8 = 8x - 4.
10x - 8x = -4 + 8.
2x = 4.
x = 4/2.
x = 2.
The total number of beans Ethan had at the end is 5x + 8x = 13x = 13(2) = <<5*2+8*2=26>>26. Answer: \boxed{26}.