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 140 in week 1, to 140 + d in week 2, to 140 + 2d in week 3 and so on, until the company is producing 206 in week 12. (a) Find the value of d. After week 12 the company plans to continue making 206 bicycles each week. (b) Find the total number of bicycles that would be made in the first 52 weeks starting from and including week 1.

A-Level Edexcel Maths Pure Trigonometric Identities: A company, which is making 140 b

A company, which is making 140 bicycles each week, plans to increase its production - Edexcel - A-Level Maths Pure - Question 5 - 2017 - Paper 1

Question 5

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 5 - 2017 - Paper 1

Step 1

(a) Find the value of d.

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Answer

To find the value of d, we need to utilize the condition that the company produces 206 bicycles in week 12. We can express the number of bicycles produced in week 12 using the following equation:

$206 = 140 + (12 - 1)d$

This simplifies to:

$206 = 140 + 11d$

Now, subtract 140 from both sides:

$66 = 11d$

Now, divide both sides by 11:

$d = 6$

Step 2

(b) Find the total number of bicycles that would be made in the first 52 weeks starting from and including week 1.

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Answer

After week 12, the company will continue to produce 206 bicycles per week. We can break this down into two parts:

Weeks 1 to 12: The number of bicycles produced each week is:
- Week 1: 140
- Week 2: 140 + 6 = 146
- Week 3: 140 + 2(6) = 152
- ...
- Week 12: 206
The total for weeks 1 to 12 is the sum of this arithmetic series: We can use the formula for the sum of an arithmetic series: $S_{n} = \frac{n}{2} (a + l)$ where:
- n = number of terms = 12
- a = first term = 140
- l = last term = 206 Plugging in the values: $S_{12} = \frac{12}{2} (140 + 206) = 6 \times 346 = 2076$
Weeks 13 to 52: The company will produce 206 bicycles every week, for a total of:
- Number of weeks = 52 - 12 = 40
- Total bicycles = 206 bicycle/week * 40 weeks = 8240

Thus, the total number of bicycles produced in the first 52 weeks is:

$Total = 2076 + 8240 = 10316$

A company, which is making 140 bicycles each week, plans to increase its production - Edexcel - A-Level Maths Pure - Question 5 - 2017 - Paper 1

Worked Solution & Example Answer:A company, which is making 140 bicycles each week, plans to increase its production - Edexcel - A-Level Maths Pure - Question 5 - 2017 - Paper 1

(a) Find the value of d.

(b) Find the total number of bicycles that would be made in the first 52 weeks starting from and including week 1.

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