Question

A local bassball tournament includes in-state and out-of-state baseball teams. the ratio of in-state teams to the total number of teams in the tournament is 1:5. There are 8 out-of-state teams in the tournament. How many teams are in the tournament altogether?

[A] 8
[B] 10
[C] 9
[D] 32

Answer 1

[B] There are total 10 teams in the in the tournament altogether.

Explanation:

Let us assume there are total m teams in tournament altogether.

Now, Ratio of in-state teams : Total number of teams = 1: 5 ..... (1)

Number of out state teams = 8

Now, as we know that

Total number of teams = Number of { in- state teams + out - state teams}

or, m = Number of in -state team + 8

⇒Number of in -state team = m - 8

⇒Ratio of in-state teams : Total number of teams = (m-8) : m .... (2)

By the RATIO OF PROPORTIONALITY:

both equation (1) and (2) represent the same ratio.

⇒ 1: 5 = (m-8) : m

or,
`(1)/(5)   = ((m-8))/(m) \\\implies m = 5(m-8)`

or, m = 5 m - 40

or, 4 m = 40

⇒ m = 40 /4 = 10 , or m = 10

Hence, there are total 10 teams in the in the tournament altogether.