Question 1201120
120 oranges in box A and box B.
2/3 of the oranges in box A were big and the rest small.
4/9 of the oranges in box B were big and the rest small.
there were an equal number of small oranges in both boxes.


let a equal the numbr of oranges in box A.
let b equal the number of oranges in box B.
you get a + b = 120.


number of big oranges in box A = 2/3 * a
number of small oranges in box A = 1/3 * a


number of big oranges in box B = 4/9 * b
number of small oranges in box B = 5/9 * b


the number of small oranges in box A is equal to the number of small oranges in box B.
you get:
1/3 * a = 5/9 * b


solve for a in that equation to get:
a = 15/9 * b = 5/3 * b
since a + b = 120, you get:
5/3 * b + b = 120 by replacing a with 5/3 * b.
this results in 8/3 * b = 120
solve for b to get b = 120 * 3/8 = 45.
since a + b = 120, you get a = 75, because 75 + 45 = 120.


since a =  75, then 2/3 * a = 50
since b = 45, then 4/9 * b = 20
total big oranges in both boxes is 70.
that's your solution.


the breakdown is:


big oranges in box A = 50
small oranges in box A = 25


big oranges in box B = 20
small oranges in box B = 25


equal number of small oranges in both boxes confirms the solution is correct.