Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#9

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Question

A farmer has a pay scheme to keep fruit pickers working throughout the 30 day season. He pays £a  for their first day, £(a + d ) for their second day, £(a + 2d ) for their third day, and so on, thus  increasing the daily payment by £d for each extra day they work. A picker who works for all 30 days  will earn £40.75 on the final day.

a.   Use this information to form an equation in a and d.

A picker who works for all 30 days will earn a total of £1005

b.   Show that 15(a + 40.75) = 1005

c.   Hence find the value of a and the value of d.

Solution

a.
 

From the given information we can collect following data about the said arithmetic sequence.

First day earning of a fruit picker is £a.

Second day earning of a fruit picker is £(a+d).

Third day earning of a fruit picker is £(a+d).

We can see that daily earnings of a fruit picker form an arithmetic sequence.

We are given that a picking goes on throughout the 30 day season. That means for each picker  there would be 30 payments.

We are given that a picker who works for all 30 days will earn £40.75 on the final day.

Expression for the general term  in the Arithmetic Progression (A.P) is:

Therefore;

b.
 

A picker who works for all 30 days will earn a total of £1005.

Therefore, sum of all 30 terms of payments to a picker is £1005.

Expression for the sum of  number of terms in the Arithmetic Progression (A.P) is:

Therefore;

c.
 

We are required to find the values of a and d.

We have found two equations in (a) and (b) involving a and d. We can solve these two simultaneous  equations.

We can find value of a from first equation.

We substitute this value of a in second equation.

Therefore, every picker received £0.5 more every next day.

We can substitute this value of d in first equation to find value of a.

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