Question

Gaya spends $48 to buy books that cost Sx each.
(a) Write down an expression, in terms of x, for the number of books Gaya buys.
(b) Myra spends S60 to buy books that cost S(x+2) each.
Gaya buys 4 more books than Myra.
Show that x^2+5x-24 = 0.

Answer 1

The relationships between the amount spent on books and the cost of

each book is a proportional relationship.

The correct responses are;

• $(a) \ \displaystyle \mathrm{The \ number \ of \ books \ Gaya \ buys \ is } \ \underline{\frac{48}{x} \ books}$

• $\mathrm{(b) \displaystyle \underline{ \left(\frac{48}{x} -4 \right) \cdot \left(x + 2 \right) - 60 = x^2 - 5 \cdot x - 24 = 0}}$

Reasons:

The amount Gaya spends on books = $48

The cost of each book = $ x

(a) The expression in terms of x for the number of books Gaya buys is therefore;

Number of books Gaya buys × $ x = $48

Therefore;

• $\displaystyle Number \ of \ books \ Gaya \ buys = \frac{\ 48}{\ x}$

(b) The amount Myra spends to buy books = $60

The cost of each book = $·(x + 2)

The number of books Myra buys = The number of books Gaya buys - 4

We have;

$\displaystyle Number \ of \ books \ Myra \ buys = \frac{48}{x} - 4$

Which gives;

$\displaystyle \mathbf{\left(\frac{48}{x} - 4 \right) \cdot \left(x + 2 \right)} = 60$

Using a graphing calculator, we get;

$\displaystyle \frac{4 \cdot x^2 - 20 \cdot x - 96}{x} = 60$

4·x² - 20·x - 96 = 60·x

Which gives;

4·x² + 40·x - 60·x - 96 = 0

4·x² - 20·x - 96 = 0

x² - 5·x - 24 = 0

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