Problem 13 · 2001 AMC 8
Hard
Fractions, Decimals & Percents
proportion
Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?
Show answer
Answer: D — 50 degrees.
Show hints
Hint 1 of 2
A pie slice's angle is just that group's share of the full circle — students and degrees rise together in lockstep.
Still stuck? Show hint 2 →
Hint 2 of 2
With 36 students splitting 360°, each student is worth 360 ÷ 36 = 10° — a clean conversion factor that turns the whole problem into easy counting.
Show solution
Approach: students → fraction of 360°
- First find the cherry count. The leftover after the named pies is 36 − 12 − 8 − 6 = 10 students, and half of those pick cherry, so 5 students.
- Set up the "per-student" rate once: 360° ÷ 36 students = 10° each. Cherry's 5 students take 5 × 10° = 50°.
- The slick part is the 10°-per-student rate: with 36 students in 360°, the numbers are tailor-made to cancel. Whenever a count divides 360 evenly, find the degrees-per-item first and the rest is multiplication.
Another way — fraction of the whole circle:
- Cherry is 5 of 36 students, a fraction 5/36 of the class.
- Apply that same fraction to the full circle: (5/36) × 360° = 50°.
Mark:
· log in to save