In the year 2000 a shop sold 150 computers - Edexcel - A-Level Maths Pure - Question 10 - 2014 - Paper 1

To calculate the total sales from 2000 to 2013, we first determine the total number of years:

• Total years = 2013 - 2000 + 1 = 14 years.

Using the formula for the sum of an arithmetic series:

$S_n = \frac{n}{2} (a + l)$

where:

• $n$ = number of terms = 14,
• $a$ = first term = 150,
• $l$ = last term = 150 + (14 - 1) \times 10 = 150 + 130 = 280.

Calculating the total:

$S_{14} = \frac{14}{2} (150 + 280) = 7 \times 430 = 3010$

Thus, the total number of computers sold from 2000 to 2013 is 3010.

Let the number of computers sold in that particular year be $x$.

The selling price in that year can be expressed as:

• Selling price = £900 - £20y (where $y$ is the number of years since 2000).

So:

$\text{Selling price} = 900 - 20(y)$

Also, the number of computers sold can be represented as:

$x = 150 + 10y$

Setting up the equation:

$900 - 20y = 3(150 + 10y)$

Expanding and solving for $y$:

$900 - 20y = 450 + 30y$

Combining like terms gives:

$450 = 50y$

Thus, $y = \frac{450}{50} = 9$.

Since $y$ represents the years since 2000, we find:

The year is 2000 + 9 = 2009.