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10 Paul and Selina each have $x. Later, each person has more money and the product of their money is 12x2 − 8x − 15.
(a)   Factorise the expression.
(b)   Find how much money each person had initially if Paul now has $65 and Selina has $17.

Please explain, in detail how to get the answer for B.

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1 Answer

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For a), we obviously have (6x + 5)(2x - 3)

The question explains that the expression is the product of their money. Since we have factorised it, we now know that one of them now has $(6x + 5) and the other must have $(2x - 3).

We find out that Paul actually has $65 at the end, compared to Selina's $17. Take it that Paul owns the $(6x + 5), since it seems to be the higher of the two. So now we solve for x in the equation:

6x + 5 = 65

x = 10

You can confirm your answer by working with Selina's money. They both had the same amount to begin, so they both produce the same result.

2x - 3 = 17

x = 10

Therefore, Paul and Selina both intially had $10.

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