Question

the school borad would like to raise the fraction of fathers on a borad from 1/3 to 1/2. this could be done by replacing 2 mothers with fathers. how many people are on the board.

Answer 1

To raise the fraction of fathers on a board from 1/3 to 1/2, the school board needs to replace 2 mothers with fathers. There are initially 12 people on the board.

Step-by-step explanation:

To raise the fraction of fathers on a board from 1/3 to 1/2, we need to replace 2 mothers with fathers. Let's assume there are 'x' people on the board initially. Since 1/3 of the board consists of fathers, the number of fathers is (1/3)x, and the number of mothers is (2/3)x. To increase the fraction of fathers to 1/2, we need to change the number of fathers to be (1/2)x.

Since we are replacing 2 mothers with fathers, the new number of mothers should be (2/3)x - 2, and the new number of fathers should be (1/3)x + 2. Setting this equal to (1/2)x, we can solve for 'x':

(1/3)x + 2 = (1/2)x
(1/3)x - (1/2)x = -2
(2/6)x - (3/6)x = -2
(-1/6)x = -2
x = (-2) / (-1/6) = 12

Therefore, there are initially 12 people on the board.