Question 1121977
there were 900 oranges and apples in a box.  When 7/9 of the oranges and 2/3 of the apples were taken out from the box, there was an equal number of oranges and apples left.  How many more oranges than apples were there at first?
<pre>Let original number of apples be A
Then original number of oranges = 900 – A
Taking out {{{7/9}}} of the oranges leaves {{{matrix(1,5, (2/9)(900 - A), "or", 2(900 - A)/9, or, ("1,800" - 2A)/9)}}}
Taking out {{{2/3}}} of apples leaves {{{matrix(1,3, (1/3)A, or, A/3)}}}
Since the numbers are then the same, we get: {{{matrix(1,3, ("1,800" - 2A)/9, "=", A/3)}}}
9A = 3(1,800 – 2A) -------- Cross-multiplying
9A = 5,400 – 6A
9A + 6A = 5,400
15A = 5,400 = 15A
Original number of apples, or A = {{{highlight_green(matrix(1,3, "5,400"/15, "=", 360))}}}  
Original number of oranges: {{{highlight_green(matrix(1,5, "900 - A,", or, 900 - 360, "=", 540))}}}
From this info. you should be able to find your answer!