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.
