Chapter 6, Problem 6PFA

To determine

To find: The correct answer out of four given answers of a given question.

Answer to Problem 6PFA

The option B has correct answers

Explanation of Solution

Given information:

The sum of two numbers is -3. Three times the first number minus the second number is 27. What are two numbers?

A. 6 and 3  B. 6 and -9  C. 12 and -15  D. 7/15 and -18

Method used:

We obtain two linear equations and solve them.

Calculations:

Suppose two numbers are x and y .

According to first given condition $x+y=-3$   ...... (1)

According to second given condition $3x-y=27$   ...... (2)

Now, adding equation (1) and (2)

  $\left(x+y\right)+(3x-y)=-3+27$

  $\Rightarrow 4x=24$

  $\Rightarrow x=\frac{24}{4}=6$

Thus, first number is 6.

Further, substituting $x=6$ in equation (1)

  $6+y=-3$

  $y=-3-6=-9$

Thus, second number is -9.

Since, the two numbers are 6 and -9, so option B is correct.

Conclusion:

The option B has correct answers.