Sam, Emily, and Ryan each baked some cupcakes to be sold at their school fête. The number of cupcakes baked by each person is represented by the pie chart. Ryan baked twice as many cupcakes as Emily. And there were 720 cupcakes baked in total. Work out the total number of cupcakes that Emily baked for the fête.
There are lots of ways of approaching this problem. One way would be to consider the angles in a pie chart. The sum of angles in a pie chart is 360 degrees, as angles in a circle add up to 360 degrees. We’re told in the question that Ryan baked twice as many cupcakes as Emily. This means that the angle for Ryan in the pie chart will be twice as big as the angle for Emily. If we let Emily’s angle be the letter 𝑥, then Ryan’s angle will be two 𝑥, as two multiplied by 𝑥 is two 𝑥.
As the three angles must sum to 360, we can set up an equation. Two 𝑥 plus 𝑥 plus 45 equals 360. Two 𝑥 plus 𝑥 is equal to three 𝑥. Therefore, three 𝑥 plus 45 equals 360. We can subtract 45 from both sides of this equation. The left-hand side becomes three 𝑥, as 45 minus 45 is zero. 360 minus 45 is equal to 315. This gives us three 𝑥 is equal to 315. We can then calculate 𝑥 by dividing both sides of the equation by three. Three 𝑥 divided by three is equal to 𝑥, and 315 divided by three is equal to 105. Therefore, 𝑥 equals 105.
The angle in a pie chart that represents Emily is 105 degrees. Two times 105 is equal to 210. This means that the angle that represents Ryan is 210 degrees. We can check these answers by adding 105, 45, and 210 and making sure they add up to 360.
We were also told in the question that there were
370  cupcakes baked in total. Therefore, 360 degrees represents 720 cupcakes. Dividing 360 degrees by 360 gives us one degree. This means that if we divide 720 by 360, we can work out how many cupcakes are represented by one degree. 720 divided by 360 is equal to two. Therefore, every one degree on the pie chart represents two cupcakes.
We were asked to work out the total number of cupcakes that Emily baked. And we know that Emily’s angle on the pie chart was 105 degrees. Multiplying one by 105 gives us 105. Multiplying two by 105 gives us 210. Therefore, 105 degrees represents 210 cupcakes. Emily baked a total of 210 cupcakes for the fête.
There is an alternative method we could’ve used once we’d would worked out the angle for Emily. As the angle that represented Emily’s cupcakes was 105 degrees and the total or sum of the angles was 360 degrees, the fraction that represents Emily is 105 out of 360. There were a total of 720 cupcakes. We can multiply this fraction by 720 to calculate the number of cupcakes that Emily baked. We could do some cross-cancelling or we could type the calculation into the calculator. Either way, we get an answer of 210. This confirms that Emily did indeed bake 210 cupcakes.