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A company, which is making 140 bicycles each week, plans to increase its production - Edexcel - A-Level Maths Pure - Question 6 - 2017 - Paper 1
Question 6
A company, which is making 140 bicycles each week, plans to increase its production. The number of bicycles produced is to be increased by d each week, starting from... show full transcript
Worked Solution & Example Answer:A company, which is making 140 bicycles each week, plans to increase its production - Edexcel - A-Level Maths Pure - Question 6 - 2017 - Paper 1
Step 1
Step 2
Find the total number of bicycles that would be made in the first 52 weeks starting from and including week 1.
Answer
From week 1 to week 12, the number of bicycles produced each week is given by:
- Week 1: 140
- Week 2: 140 + 6 = 146
- Week 3: 140 + 2(6) = 152
- ...
- Week 12: 206.
For weeks 1 to 12:
egin{align*} S_{12} &= rac{12}{2} (140 + 206) \ &= 6 imes 346 = 2076. \end{align*}
From week 13 to week 52, the company produces 206 bicycles:
egin{align*} S_{40} &= 206 imes 40 = 8240. \end{align*}
Thus, the total number of bicycles made in the first 52 weeks is:
egin{align*} Total &= 2076 + 8240 = 10316. \end{align*}