Question

These three statements are all true: 1) A x B = 12 2) A + B + C = 12 3) B - A = 1 Which of these are true? a) C = 5 b) B = 3 c) A or B = 6

Answer 1

C = 5

Step-by-step explanation

We have that:

1) A * B = 12

2) A + B + C = 12

3) B - A = 1

From 1) we have that:

A = 12 / B

Put that in 3):

`\begin{gathered} B\text{ - }\frac{12}{B\text{ }}\text{ = }1 \\ \text{Multiply through by B:} \\ B^2\text{ - }12\text{ = B} \\ \Rightarrow B^2\text{ - B - 12 = 0} \\ \text{Solve for B, we have that:} \\ B^2\text{ - 4B + 3B - 12 = 0} \\ (B\text{ - 4)(B + 3) = 0} \\ \Rightarrow\text{ B = 4 or -3} \end{gathered}`

This means that:

A = 12 / 4 = 3

or

A = 12 / -3 = -4

If A = 3, B = 4, then, from 2):

3 + 4 + C = 12

=> 7 + C = 12

C = 12 - 7

C = 5

Since A or B is not equal to 6 and B is not equal to 3, then, the only correct option is C = 5 (Option a)