Chapter 6.3, Problem 12P

In a class, 45 students take the SAT exam. The number of boys is 8 more than the number of girls.

a. Write a system that models the above situation.

b. Do you need to multiply any of the equations by a constant? If so, which equation and what is the constant?

To determine

a system that models the given situation

Answer to Problem 12P

The system of equations would be

  $\begin{array}{l}B+G=45\\ B-G=8\end{array}$

Explanation of Solution

Given information:

The total number of students = 45.

The number of girls in the class is 8 less than the number of boys in the class

Calculation:

Consider B as the number of boys and G as the number of girls. And it is given that the total number of students in the whole class is 45.

  $B+G=45$

The number of girls in the class is 8 less than the number of boys in the class

  $\begin{array}{l}B=G+8\\ B-G=8\end{array}$

Therefore the system of equations would be

  $\begin{array}{l}B+G=45\\ B-G=8\end{array}$

Conclusion:

The system of equations would be

  $\begin{array}{l}B+G=45\\ B-G=8\end{array}$

To determine

whether it is needed to multiply any equation with a constant

Answer to Problem 12P

No equations are required to be multiplied by a constant

Explanation of Solution

Given information:

The total number of students = 45.

The number of girls in the class is 8 less than the number of boys in the class

Calculation:

All the variables are eliminated here as every coefficient is 1 here for two variables

Conclusion:

No equations are required to be multiplied by a constant