Find the number such that when 3/4 of it is added to 3 1/3, the sum is the same as when 2/3 if it is subtracted from 6 1/2

Answer 1

Let's call the unknown number "x".

According to the problem:

3/4 x + 3 1/3 = 6 1/2 - 2/3 x

First, let's simplify the fractions:

3/4 x + 10/3 = 13/2 - 2/3 x

Next, let's get rid of the fractions by multiplying everything by the least common multiple of 3 and 4, which is 12:

9x + 40 = 78 - 8x

Now, let's isolate x by adding 8x to both sides and subtracting 40 from both sides:

17x = 38

Finally, we can solve for x by dividing both sides by 17:

x = 38/17

Therefore, the number we were looking for is 38/17.