A shopkeeper sells pens and pencils. Each pen costs $5 and each pencil costs $3. One day he sold $x$ pens. On the same day, he sold 9 more pens than pencils. (a) Write down an expression, in terms of $x$, for his total income from the sale of these pens and pencils. (b) This total income was less than $300. Form an inequality in $x$ and solve it. (c) Hence write down the maximum number of pens that he sold.

1. Problem Description

A shopkeeper sells pens and pencils. Each pen costs $5 and each pencil costs$

3. One day he sold $x$ pens. On the same day, he sold 9 more pens than pencils.

(a) Write down an expression, in terms of $x$, for his total income from the sale of these pens and pencils.

(b) This total income was less than $

3

0

0. Form an inequality in $x$ and solve it.

(c) Hence write down the maximum number of pens that he sold.

2. Solution Steps

(a) Let the number of pens sold be $x$. Then the number of pencils sold is $x-9$. The total income is given by the sum of the income from pens and the income from pencils.

The income from pens is $5x$ and the income from pencils is $3(x-9)$.

So, the total income is $5x + 3(x-9)$.

(b) The total income is less than $

3

0

0. Therefore, we have the inequality

$5x + 3(x-9) < 300$

$5x + 3x - 27 < 300$

$8x - 27 < 300$

$8x < 300 + 27$

$8x < 327$

$x < \frac{327}{8}$

$x < 40.875$

(c) Since the number of pens must be an integer, the maximum number of pens that he sold is

4

0.

3. Final Answer

(a) $5x + 3(x-9)$

(b) $x < 40.875$

(c) $40$