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

Answer:

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

Step-by-step 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, $\frac{1}{5}   = \frac{(m-8)}{m} \\\implies m = 5(m-8)$

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.