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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?

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Answer:

Let the number they chose be 'x'.

Result of Jane = [tex]3x -2[/tex]

Result of Elliot = [tex]2x+3[/tex]

Given that,

The product of their result = 110

[tex]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=\frac{-29}{6} \\So,~ the ~number ~they~ chose~was ~either ~4 ~or ~\frac{-29}{6}[/tex]

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