Percents and area

moonlite wrote:A circle graph shows how the budget of a certain company was spent: 63 percent for salaries, 12 percent for research and development, 6 percent for utilities, 5 percent for equipment, 4 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
(A) 10°
(B) 18°
(C) 36°
(D) 90°
(E) 324°

Please explain thanks.

If the % for transportation is "t", we can say:

t = 100 - (63 + 12 + 6 + 5 + 4)

t = 100 - 90

t = 10

If 10% of funds were used for transportation, 10% of the area of the circle will be devoted to transportation. Using the circle sector formula:

degrees(t)/360 = area(t)/area(circle)

degrees(t)/360 = 1/10

degrees(t) = (1/10)(360) = 36

Or, using common sense (often quicker than formulas on test day!), if t makes up 10% of the circle, then t should contain 10% of the 360 degrees. Again:

10%(360) = 36

Thanks, I was making it more complicated then required!