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