SOLUTION: Hi There were 120 oranges in box A and box B. 2/3 of the oranges in A were big and the rest were small. 4/9 of the oranges in B were big the rest were small. There were an equal n

Question 1201120: Hi
There were 120 oranges in box A and box B. 2/3 of the oranges in A were big and the rest were small. 4/9 of the oranges in B were big the rest were small. There were an equal number of small oranges in both boxes. How many big oranges were there altogether.
Thanks
Found 2 solutions by mananth, Theo:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Assume x oranges in A
y oranges in B
2/3 of the oranges in A were big
So 1/3 were small
A contains (1/3) x small oranges
4/9 of the oranges in B were big
S0 5/9 were small
(5/9)y = small oranges
small oranges are equal in A & B
1/3 x = 5/9 y
Y= 3/5 x
x + 3/5 x = 120 (substitute y)
8x/5 =120
X=75 oranges in A
Y=45 oranges in B

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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