Question

Q2.

I am thinking of two numbers.
The first number is x
The second number is 7.5 more than x.
Write down an expression, in terms of x for the second number.
For the two numbers,
the product is double the sum.
Work out the numbers I could be thinking of.
Give both possible pairs of answers.

Answer 1

second number = (x + 7.5)

Since the product of the two numbers is double of their sum,

x(x + 7.5) = 2(x + x + 7.5)

x² + 7.5x = 2(2x + 7.5)

x² + 7.5x = 4x + 15

x² + 7.5x - 4x - 15 = 0

x² + 3.5x - 15 = 0

∴ x = -6 or 2.5

∴ second number

= -6 + 7.5 or 2.5 + 7.5

= 1.5 or 10

∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.