SOLUTION: 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 m
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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? Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! x = number of oranges
y = number of apples.
x + y = 900
when 7/9 of the oranges and 2/3 of the apples are taken out, the number of remaining oranges is equal to the number of remaining apples.
formula for that is:
x - 7/9 * x = y - 2/3 * y
simplify to get:
2/9 * x = 1/3 * y
solve for y to get:
y = 6/9 * x
in the equation of x + y = 900, replace y with 6/9 * x to get:
x + 6/9 * x = 900
multiply both sides of this equation by 9 to get:
9x + 6x = 8100
combine like terms to get 15x = 8100
solve for x to get x = 8100 / 15 = 540
in the original equation of x + y = 900, solve for y to get y = 900 - 540 = 360.
you have x = 540 and y = 360 for a total of 900.
this translates to 540 oranges and 360 apples.
when you take out 7/9 of the oranges, you have 2/9 left.
when you take out 2/3 of the apples, you have 1/3 left.
2/9 * 540 = 120
1/3 * 360 = 120
the number of apples and oranges is now the same.
how many more oranges than apples were there at first?
there were 540 - 360 = 180 more oranges than apples at first.
You can put this solution on YOUR website! 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?
Let original number of apples be A
Then original number of oranges = 900 – A
Taking out of the oranges leaves
Taking out of apples leaves
Since the numbers are then the same, we get:
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 =
Original number of oranges:
From this info. you should be able to find your answer!
