Question

there were 1125 books sold last week at sids bookstore. the circle graph below summarizes these books by genre. the central angle for the self - help slice is 83.52°. how many of the books sold were self - help books?

Explanation:

Step1: Find proportion of Self - Help

The total degrees in a circle is \(360^{\circ}\). The proportion of Self - Help books is the ratio of the central angle of Self - Help to \(360^{\circ}\). So the proportion \(p=\frac{83.52^{\circ}}{360^{\circ}}\).

Step2: Calculate number of Self - Help books

The total number of books is \(1125\). To find the number of Self - Help books, we multiply the total number of books by the proportion of Self - Help books. So the number of Self - Help books \(n = 1125\times\frac{83.52}{360}\).
First, calculate \(\frac{83.52}{360}=0.232\). Then, \(1125\times0.232 = 1125\times(0.2 + 0.03+0.002)=1125\times0.2+1125\times0.03 + 1125\times0.002=225 + 33.75+2.25 = 261\).

Answer:

261