sushiDPT13 wrote:
A certain high school team has only sophomores juniors and seniors. The ratio of sophomores to juniors is 2:3, and the ratio of juniors to seniors is 5:6. Sophomores comprise what fraction of the whole team?
Both ratios have a value for the number of
JUNIORS.
So, to COMBINE the to ratios, we need a value for the
number of juniors that's the same in both ratios.
To do so, we'll create EQUIVALENT ratios (by multiplying both parts of a ratio by the same value)
GIVEN:
sophomores :
juniors = 2 :
3juniors : seniors =
5 : 6
Take the TOP ratio and multiply both parts of the ratio by 5.
Take the BOTTOM ratio and multiply both parts of the ratio by 3.
We get:
sophomores :
juniors = 10 :
15juniors : seniors =
15 : 18
We can now COMBINE the ratios to get: sophomores :
juniors : seniors = 10 :
15 : 18
10 +
15 + 18 = 43
So, out of every 43 players on the whole team, 10 players are sophomores.
Answer: 10/43
Cheers,
Brent