When 2/3 of a number is increased by 20, the sum is then halved, the result obtained is the same as 2/3 of the number, increased by 3. find the number.

Set up

(2/3)x + 20      This represents 2/3 of a number increased by 20.

1/2( (2/3)x + 20 )   This represents the sum is halved

then that is the same as 2/3(x) + 3

1/2( (2/3)x + 20 ) = (2/3)x + 3     Multiply the left by 1/2

(1/2 * 2/3)x + 1/2*20 = (2/3)x + 3

(1/3)x + 10 = (2/3)x + 3                 You don't have to do this but it might be nice to get rid of the fractions, so multiply both sides by 3

x + 30 = 2x + 6                            Subtract x from both sides.

x - x + 30 = 2x - x + 6                  Combine

30 = x + 6                                     Subtract 6 from both sides.

30 - 6  = x + 6 - 6                         Combine

24 = x

Check

LHS

(1/2)(2/3)x + 20 * 1/2

1/2 * 2/3 x + 20*1/2

1/3 x + 10

1/3 * 24 + 10

8 + 10

18

RHS

2/3 * 24 + 3

16 + 3

18 They do check.

Remark. Don't try to understand the problem all at once. Read it through once. You are trying to figure out only where the phrases of information begin and end. Then start writing down the results of each phrase.