Question 1121977
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.