Question

Veena and Naveed thought of a number each. Veena's number is 3 less than twice Naveed's number. If the product of their numbers is 2, which of these could be Veena's number?​

Answer 1

Given:

Veena and Naveed thought of a number each

Veena's number is 3 less than twice Naveed's number

If the product of their numbers is 2

To find:

Which of these could be Veena's number?​

Solution:

Let's assume,

"x" → number thought by Veena

"y" → number thought by Naveed

We have, Veena's number is 3 less than twice Naveed's number, so the equation that can be formed is:

x = 2y - 3 ..... (i)

Also, we have, the product of their numbers is 2, so the equation that can be formed is:

xy = 2

substituting from (i)

⇒ (2y - 3) y = 2

⇒ 2y² - 3y = 2

⇒ 2y² - 3y - 2 = 0

⇒ 2y² - 4y + y - 2 = 0

⇒ 2y(y - 2) + 1(y - 2) = 0

⇒ (2y + 1)(y - 2) = 0

⇒ y = $-\frac{1}{2}$ or 2

Now,

When y = $-\frac{1}{2}$,

∴ x = 2y - 3 = [2 × ( $-\frac{1}{2}$)] - 3 = - 1 - 3 = - 4

and

When y = 2,

∴ x = 2y - 3 = [2 × 2] - 3 = 4 - 3 = 1

Since we are not given the options and also we do not have any information about whether the number Veena thought is positive or negative.

Thus, the number thought by Veena could be - 4 or 1.

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