Question

a) Set up an algebraic equation that could represent the following life situation: (5)

Nkateko sells bananas at the low but fixed price of R3/kg. In order to ensure that she makes a reasonable profit, she adds a certain fixed amount of money to any quantity of bananas purchased. A customer who bought 4 kg of bananas was observed paying R14

b) Draw the situation for which the equation was set up in (b) above. You should be able to use this drawing to explain the situation clearly to a learner as part of remedial work. (5)

Answer 1

a)

Fixed price per kg = R $3$

Let certain fixed amount that is added be $C$

Let $a$ customers buy $x$ kg

Let amount to be paid be R $y$

$y= 3x+C$

Now hence,

$x= 4$

$y= 14$

$14=3(4)+C$

$C= 2$

Hence equation is

$y= 3x+2$

Where $y$ is the total amount and $x$ is number of kg

b)

At point A, y=2. This shows the fixed cost added to any quantity

At point R, y=14. This shows the total revenue earned by Nkateko

At point Q, x=4. This shows the quantity Nkateko sold.