Question

Mr.Jared asked his math students to compute the numerical value of(a+3).(a+6)for a particular positive value of a Ruby accidentally copied the expression as(a+3)a+6,so even though she used the correct value for a and did all computations correctly,she got the wrong answer.Similarly,Amber mistakenly wrote the expression as a+3.(a+6)and obtained an incorrect answer,despite making no other mistakes.Curiously,Ruby and Amber ended up with the same wrong answer!What was the correct answer to Mr.Jared'squestion?

Answer 1

The correct answer is 70.

Explanation:

Since they got the same answer we have the equation:

(a + 3)a + 6 = a + 3(a + 6)

a^2 + 3a + 6 = a + 3a + 18

a^2 + 3a - 3a -a + 6 - 18 = 0

a^2 - a - 12 = 0

(a - 4)(a + 3) = 0

So a = 4 or -3.

As a is given as positive we take a = 4.

The correct numerical value =

(4 + 3)( 4 + 6)

= 70.