We are given four problems involving ratios and fractions. a. Find the ratio of big fish to little fish in a pond with 240 little fish and 90 big fish. b. Find the boy-girl ratio in a class of 30 students where 14 are girls. c. Find the win-loss ratio of a team that won $3/8$ of its games and lost the rest. d. Find the fraction of blue marbles if the ratio of red to blue marbles is 5 to 3.

1. Problem Description

We are given four problems involving ratios and fractions.

a. Find the ratio of big fish to little fish in a pond with 240 little fish and 90 big fish.

b. Find the boy-girl ratio in a class of 30 students where 14 are girls.

c. Find the win-loss ratio of a team that won $3/8$ of its games and lost the rest.

d. Find the fraction of blue marbles if the ratio of red to blue marbles is 5 to

3.

2. Solution Steps

a. The ratio of big fish to little fish is $90:240$. We can simplify this ratio by dividing both sides by their greatest common divisor, which is

3

0.

$90/30 = 3$

$240/30 = 8$

So, the ratio is $3:8$.

b. There are 30 students in total, and 14 are girls. Therefore, the number of boys is $30 - 14 = 16$. The boy-girl ratio is $16:14$. We can simplify this by dividing both sides by their greatest common divisor, which is

2.

$16/2 = 8$

$14/2 = 7$

So, the ratio is $8:7$.

c. The team won $3/8$ of its games. This means they lost $1 - 3/8 = 8/8 - 3/8 = 5/8$ of their games. Therefore, the win-loss ratio is $(3/8):(5/8)$, which simplifies to $3:5$.

d. The ratio of red marbles to blue marbles is $5:3$. This means that for every 5 red marbles, there are 3 blue marbles. The total number of marbles representing one group in the ratio is $5 + 3 = 8$. The fraction of blue marbles is the number of blue marbles divided by the total number of marbles, which is $3/8$.

3. Final Answer

a. $3:8$

b. $8:7$

c. $3:5$

d. $3/8$