Question

Two friends are playing tic-tac-toe. If Amy wins 3/8 of the time, Lily wins 3/10 of the time, and they tie the rest of the time, then what fraction of the time do they tie?

Answer 1

13/40

Explanation:

The period they have played can be divided into 3 parts:

● The time Amy wins

● The time Lily wins

● The time they tie

So the sum of them is the total time of playing.

Let A be the time Amy wins, L the tile Lily wins and T the time they tie .

●●●●●●●●●●●●●●●●●●●●●●●

Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.

So:

A + P + T = 1

3/8 + 3/10 + T = 1

Multiply 8 by 10 and 10 by 8 so that you get a common denominator.

Cross multiply the numerators and the denominators.

(3*10+3*8)/80 + T = 1

(30 + 24)/80 + T =1

54/80 + T = 1

(27*2)/(40*2) + T = 1

Simplify by 2

27/40 + T = 1

T = 1 - 27/40

Multiply one by 40 to get a common denominator

T = (40-27)/40

T = 13/40

So they have tied 13/40 of the time