A farmer has a pay scheme to keep fruit pickers working throughout the 30 day season - Edexcel - A-Level Maths Pure - Question 11 - 2010 - Paper 1

The total earnings over 30 days can be calculated by finding the sum of an arithmetic series where:

• The first term is £a
• The last term is £(a + 29d)
• The number of terms is 30

The sum can be given by the formula:

$S_n = \frac{n}{2} (a_1 + a_n)$

Thus, we have:

$S_{30} = \frac{30}{2} [a + (a + 29d)] = 15[2a + 29d]$

Setting this equal to the total earnings:

$15(2a + 29d) = 1005$

From part (a), we already have:

$a + 29d = 40.75$

Now substituting this into the earnings formula:

$15(2a + 29d) = 15[2a + (40.75 - a)] = 15(a + 40.75)$

Setting this equal to 1005 gives:

$15(a + 40.75) = 1005$

From the equation in part (c), we can isolate the variable a:

$a + 40.75 = \frac{1005}{15} = 67$

Thus,

$a = 67 - 40.75 = 26.25$

Now substituting a back into the equation from part (a):

$26.25 + 29d = 40.75$

Solving for d yields:

d = \frac{14.5}{29} = 0.5$$ Hence, the values are: - a = £26.25 - d = £0.50