Question

105 students were divided equally into 15 teams.
A. how many players were on each team?
B. if each team had 3 girls, how many boys were there altogether?

Answer 1

Hint: We use the long division method to find the number of players in each team. We take 105 as dividend and 15 as divisor. Then we find the total number of girls in the batch. We subtract it from 105 to find the total number of boys.

Complete step-by-step solution:
We have the numbers of students in total. The number is 105. Those students were divided equally into 15 teams. We need to find the number of players each team has.
We find the solution by dividing the number 105 by 15.
Here 105, the number of students acts as the dividend. The number of teams acts as the divisor. We need to find the quotient of ${\displaystyle \frac{105}{15}}$.
We use the method of long division to find the solution.
$15\stackrel{7}{\stackrel{―}{)\begin{array}{rl}& 105\\ & \underset{―}{105}\\ & 0\end{array}}}$
So, three are 7 players on each team.
Now we have been given that if each team had 3 girls then we need to find how many boys were there altogether.
There are 15 teams. Each team has 3 girls. The total number of girls will be equal to the multiplication of the numbers 15 and 3.
The multiplication gives $15\times 3=45$.
This means there are 45 girls in the batch of 105 students. Therefore, the rest of the students are boys. The number of boys in total is $105-45=60$.

Note: We can also use the ratio method to solve the division ${\displaystyle \frac{105}{15}}$.
For our given fraction ${\displaystyle \frac{105}{15}}$, the G.C.D of the denominator and the numerator is 15. Now we divide both the denominator and the numerator with 15 and get ${\displaystyle \frac{{}^{105}/{}_{15}}{{}^{15}/{}_{15}}}={\displaystyle \frac{7}{1}}=7$.