This pie chart shows how the employees of a business travel to work. (a) Find the ratio of the number of employees who cycle to work to the number of employees who walk to work. Give your answer in its simplest form. (b) 80 employees travel to work by car. Work out the number of employees who cycle to work and the number of employees who walk to work.

GCSE OCR Maths 3D trigonometry: This pie chart shows how the emp

This pie chart shows how the employees of a business travel to work - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

Question 11

This pie chart shows how the employees of a business travel to work. (a) Find the ratio of the number of employees who cycle to work to the number of employees who ... show full transcript

Worked Solution & Example Answer:This pie chart shows how the employees of a business travel to work - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

Step 1

Find the ratio of the number of employees who cycle to work to the number of employees who walk to work.

96%

114 rated

Answer

To find the number of employees who cycle and walk, we first need to determine the angles representing each group in the pie chart.

The angle for cycling is given as 72°.
The angle for walking is 48°.

Next, we calculate the total angle of the pie chart, which is always 360°. Using the proportion of the angles:

Number of employees who cycle: $\text{Number of cyclists} = \frac{72}{360} \times \text{Total employees}$

Number of employees who walk: $\text{Number of walkers} = \frac{48}{360} \times \text{Total employees}$

Thus, the ratio of cyclists to walkers is: $\text{Ratio} = \frac{72}{48} = \frac{3}{2}$

The simplest form is therefore 3:2.

Step 2

Work out the number of employees who cycle to work and the number of employees who walk to work.

99%

104 rated

Answer

Given that 80 employees travel by car, we can find the total number of employees by first calculating the angles for cycling and walking:

Total angle for cycling: 72°
Total angle for walking: 48°
Total angle for car: 240°

Since the car angle represents the 80 employees: $\frac{240}{360} = \frac{80}{\text{Total employees}}$ Thus, Total employees = ( \frac{80 \times 360}{240} = 120 ).

Now we can find the number of employees who cycle and walk:

Number of cyclists:

- Number of walkers: $$\frac{48}{360} \times 120 = 16\ Thus, the final counts are: - Employees who cycle to work: 24 - Employees who walk to work: 16.

This pie chart shows how the employees of a business travel to work - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

Worked Solution & Example Answer:This pie chart shows how the employees of a business travel to work - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

Find the ratio of the number of employees who cycle to work to the number of employees who walk to work.

Work out the number of employees who cycle to work and the number of employees who walk to work.

Join the GCSE students using SimpleStudy...