In the year 2000 a shop sold 150 computers - Edexcel - A-Level Maths Pure - Question 9 - 2014 - Paper 1

To calculate the total number of computers sold from 2000 to 2013, we need to determine the number of terms and use the sum formula for an arithmetic sequence:

1. Find the total number of years from 2000 to 2013: $n = 14$ (inclusive).

2. Use the sum formula: $S_n = \frac{n}{2}(a + l)$ Where:

   • $n = 14$
   • $a = 150$ (in 2000)
   • $l = 150 + (14-1) \cdot 10 = 150 + 130 = 280$ (in 2013)

3. Now calculate: $S_{14} = \frac{14}{2}(150 + 280) = 7 \cdot 430 = 3010$

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

Let the number of computers sold in a particular year be $x$. The selling price in the year is given as:

$900 - 20(n - 1)$

Where $n$ is the number of years since 2000. We set up the equation based on the condition:

$\frac{900 - 20(n - 1)}{5} = 3x$

Now substituting $x$:

$x = 150 + (n - 1) \cdot 10$

Plugging this into the equation leads us to:

1. Replace $x$: $\frac{900 - 20(n - 1)}{5} = 3(150 + (n - 1) \cdot 10)$

After simplifying and solving, we find that $n = 9$ leads us to the year 2009. Hence, the year when the condition holds true is 2009.