Question

Polly surveyed 850 teenagers to find out their favorite type of music. She found that 32% of the teenagers surveyed like hard rock.

Part A: How many teenagers surveyed like hard rock? Show your work. (4 points)

Part B: In another survey, Damian found that 75% of the total number of teenagers surveyed like pop music. If 150 teenagers like pop music, what is the total number of teenagers that Damian surveyed? Show your work. (4 points)

Part C: Give an example of a situation in which a percentage is greater than 100%. (2 points)

Answer 1

@Holly

Answer 2

please do not copy-paste my work.

let's review quickly what "percent" (%) means. percent = per 100. ex: 50% literally means 50 per 100, or 50/100, or 0.5 as a decimal. to find a percent of a whole, multiply the percent by the whole. (ex: 50% of 100 = (50/100) * 100 = 50)

now, let's apply this to the problem:

part A) the problem states that 32% of teenagers out of 850 like hard rock. to find the # of teenagers, simply find 32% of 850, or in other words, (32/100) * 850

part B) 75% of some # of teenagers like pop music. let's let x = the number of teenagers. it says 150 teenagers like pop music, so 75% of x = 150

in other words, 0.75*x = 150, solve for x

part C) I'll just go ahead and explain this one - you might think that 100% might be the maximum percent (after all, 100% includes every part in a whole). however, sometimes we use more than 100% to describe certain situations. if a quantity doubles, that's a 100% increase, and if a quantity triples, that's a 200% increase.

for proof of this, let's let the original amount be x. if it triples to 3x, that's an increase of (3x - x = 2x). as a percentage, 2x is 2x/x = 2, or 200%.