A library received $1,300 grant. It spends 10% of the grant on magazine subscriptions, 35% on new books, 15% to repair damaged books, 30% to buy new furnitu...
Question 1 Report
A library received $1,300 grant. It spends 10% of the grant on magazine subscriptions, 35% on new books, 15% to repair damaged books, 30% to buy new furniture and 10% to train library staff.
(a) Represent this information on a pie chart.
(b) Calculate, correct to the nearest whole number, the percentage increase of the amount for buying books over that of new furniture.
Answer Details
(a) Pie chart
The whole grant of \($1{,}300\) is represented by the full circle, \(360^{\circ}\). Each item's sector angle is found from \(\text{angle}=\dfrac{\text{percentage}}{100}\times360^{\circ}\), which is the same as \(\dfrac{\text{amount}}{1300}\times360^{\circ}\).
| Item | Percentage | Amount ($) | Sector angle |
|---|---|---|---|
| Magazine subscriptions | 10% | 130 | \(\frac{130}{1300}\times360^{\circ}=36^{\circ}\) |
| New books | 35% | 455 | \(\frac{455}{1300}\times360^{\circ}=126^{\circ}\) |
| Repair of damaged books | 15% | 195 | \(\frac{195}{1300}\times360^{\circ}=54^{\circ}\) |
| New furniture | 30% | 390 | \(\frac{390}{1300}\times360^{\circ}=108^{\circ}\) |
| Staff training | 10% | 130 | \(\frac{130}{1300}\times360^{\circ}=36^{\circ}\) |
| Total | 100% | 1300 | \(360^{\circ}\) |
Drawing a circle and marking each sector in turn with the angles above gives the following pie chart:
(b) Percentage increase of books over furniture
Amount for new books \(=35\%\) of \(1300 = \$455\).
Amount for new furniture \(=30\%\) of \(1300 = \$390\).
The increase in the amount is \(455-390=\$65\), and this is expressed as a percentage of the furniture amount:
\[\text{Percentage increase}=\frac{455-390}{390}\times100\%=\frac{65}{390}\times100\%=16.67\%\approx 17\%\]The books allocation is about \(17\%\) more than the furniture allocation (to the nearest whole number).
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