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9. The price of a pen is R9.75, and a pencil costs R3.25.

a) What is the total cost if you buy a pen and a pencil?

b) What will it cost to buy 3 pens and 4 pencils?

c) Write down the total cost when you buy x pens and y pencils.

d) If you spend R68.25 on pens, how many pens did you buy?

e) If you spend Rz on pencils, how many pencils did you buy?

f) If you spend a total of R65 on pens and pencils, write down the possible combinations of the number of pens and pencils that you could have bought.

Answer :

Let's break down the problem step by step:

a) What is the total cost if you buy a pen and a pencil?

The price of a pen is [tex]R9.75[/tex], and a pencil costs [tex]R3.25[/tex]. To find the total cost of buying one pen and one pencil, add their prices:

[tex]\text{Total cost} = 9.75 + 3.25 = R13.00[/tex]

b) What will it cost to buy 3 pens and 4 pencils?

Calculate the cost of 3 pens and 4 pencils separately and then add them together:


  • Cost for 3 pens: [tex]3 \times 9.75 = R29.25[/tex]

  • Cost for 4 pencils: [tex]4 \times 3.25 = R13.00[/tex]


Add them to find the total cost:

[tex]\text{Total cost} = 29.25 + 13.00 = R42.25[/tex]

c) Write down the total cost when you buy [tex]x[/tex] pens and [tex]y[/tex] pencils.

If you buy [tex]x[/tex] pens and [tex]y[/tex] pencils, the cost can be expressed as:

[tex]\text{Total cost} = 9.75x + 3.25y[/tex]

d) If you spend [tex]R68.25[/tex] on pens, how many pens did you buy?

Let the number of pens be [tex]n[/tex]. Then:

[tex]9.75n = 68.25[/tex]

Divide both sides by [tex]9.75[/tex] to solve for [tex]n[/tex]:

[tex]n = \frac{68.25}{9.75} = 7[/tex]

So, you bought 7 pens.

e) If you spend [tex]Rz[/tex] on pencils, how many pencils did you buy?

Let the number of pencils be [tex]m[/tex]. Then:

[tex]3.25m = Rz[/tex]

Solve for [tex]m[/tex]:

[tex]m = \frac{Rz}{3.25}[/tex]

f) If you spend a total of [tex]R65[/tex] on pens and pencils, write down the possible combinations of the number of pens and pencils that you could have bought.

The equation representing this situation is:

[tex]9.75x + 3.25y = 65[/tex]

To find integer solutions for [tex]x[/tex] and [tex]y[/tex], we can try different values for [tex]x[/tex] and solve for [tex]y[/tex]:


  1. If [tex]x = 5[/tex]:
    [tex]9.75(5) + 3.25y = 65 \\
    48.75 + 3.25y = 65 \\
    3.25y = 16.25 \\
    y = 5[/tex]
    Combination: 5 pens and 5 pencils.


  2. If [tex]x = 6[/tex]:
    [tex]9.75(6) + 3.25y = 65 \\
    58.50 + 3.25y = 65 \\
    3.25y = 6.50 \\
    y = 2[/tex]
    Combination: 6 pens and 2 pencils.



These are the possible combinations when spending exact [tex]R65[/tex] on pens and pencils. Both solutions are valid as they result in an integer number of items.

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Rewritten by : Brahmana