The Bassey family's monthly budget of $2400 is split between rent, food, savings and other costs. The pie chart shows the angle at the centre for each categ...
Question 1 Report
The Bassey family's monthly budget of $2400 is split between rent, food, savings and other costs. The pie chart shows the angle at the centre for each category.
- Show that the rent sector represents $1080 of the monthly budget. (2)
- Work out the amount spent on food each month. (2)
- Work out the amount put into savings each month. (1)
- The family decide to increase their monthly savings by $120, taking this extra amount from other costs. Work out the new angle that would represent other costs on the pie chart. (1)
Answer Details
In a pie chart, each sector's angle is the same fraction of \(360^\circ\) as that category's spending is of the whole budget. So the amount for any sector is found by taking (sector angle \(\div\) 360) of the total budget.
- \(\dfrac{162}{360} \times 2400 = 1080\), showing the rent sector represents \(\$1080\). [2 marks]
- \(\dfrac{90}{360} \times 2400 = 600\), so \(\$600\) is spent on food. [2 marks]
- \(\dfrac{72}{360} \times 2400 = 480\), so \(\$480\) is put into savings. [1 mark]
- Other costs currently equal \(\dfrac{36}{360} \times 2400 = \$240\). Moving \(\$120\) of this into savings leaves \(240 - 120 = \$120\) for other costs. As a fraction of the budget this is \(\dfrac{120}{2400}\), so the new angle is \(\dfrac{120}{2400} \times 360 = 18^\circ\). [1 mark]
A dollar amount and its pie-chart angle are always directly proportional to each other, since both represent the same fraction of the whole; a change to one (as in part (d)) automatically implies a matching change to the other, found using the same \(\div 360\) or \(\div\) total conversion.
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