Question

Jane multiplies her number by three and subtracts 2.

Elliot multiplies his number by 2 and adds 3.
When they multiply their results together, the product is 110.
They both chose the same number to start with. What was their number?

Answer 1

Let the number they chose be 'x'.

Result of Jane =
`3x -2`

Result of Elliot =
`2x+3`

Given that,

The product of their result = 110

`or, (3x-2)(2x+3) = 110\\or, 6x^(2) +9x-4x-6 = 110\\or, 6x^(2) +5x - 6 = 110\\or, 6x^(2) +5x - 6-110 = 0\\\\or, 6x^(2) +5x - 116 = 0\\or, 6x^(2) +29x - 24x - 116 = 0\\or, x (6x +29) -4(6x+29) = 0\\or, (x-4)(6x+29) = 0\\i.e. x=4 or x=(-29)/(6) \\So,~ the ~number ~they~ chose~was ~either ~4 ~or ~(-29)/(6)`