help me ……………..

Question

There are some oranges and apples at a fruit stall. The ratio of the number of oranges to apples is 6:5. After 24 oranges and 23 apples are sold, the number of apples becomes 2/3 of the number of oranges. How many apples are left in the end?

Answer 1

Let x be the constant of proportionality for the ratio between oranges and apples. The fact that oranges to apples is 6:5 means that the number of each fruit starting out could be 12 and 10 (x = 2), or 18 to 15 (x = 3), etc.

So the number of oranges starting out can be represented by 6x, the number of apples by 5x. Note that 6x/5x = 6/5, i.e. the ratio reduces to 6:5.

Now after giving away 24 oranges and 23 apples, the new expressions representing the amount of each fruit remaining is:

6x - 24 (the number of oranges remaining)

5x - 23 (the number of apples remaining).

At this point the number of apples is 2/3 of the number of oranges.

5x - 23 = (2/3)(6x - 24)

Since the denominator of the fraction 2/3 divides both terms inside the parentheses, go ahead an distribute:

5x - 23 = 4x - 16

x = 7

The number of oranges starting out is: 6(7) or 42.

The number of apples starting out is 5(7) or 25.

Now give away 24 oranges, so the current number of oranges is 42 - 24 = 18.

Give away 23 apples, so the current number of apples is 35 - 23 = 12.

Note that 12 is 2/3 of 18. Check.