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

Answer 1

Let's call the number we're trying to find "x".

According to the problem:

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

We can simplify this equation by first changing all the mixed numbers to improper fractions:

3/4 x + 7/2 = 13/2 - 2/3 x

Next, let's get rid of the fractions by multiplying everything by the LCD, which is 12:

9x + 42 = 78 - 8x

Now we can solve for x:

9x + 8x = 78 - 42

17x = 36

x = 36/17

So the answer is approximately 2.12.