Question

unit 3 unit rate & percentages: end of unit study guide
for all questions: write your answer(s) on the line.

1. there are 18 pieces of candy in a bowl and 12 of them are chocolate. what percentage of the pieces of candy in the bowl are chocolate?

a. 0.66% c. 6.7%
b. 12% d. 67%
2-4. select all of the trips that would take 4 hours.
a. bike 4 miles per hour to school, which is 0.5 miles away.
b. drive 64 miles per hour between st. paul and green bay, which are 256 miles apart.
c. take a subway going 55 mph from manhattan to cape cod, which are 220 miles apart.

1. lin’s family has completed 40% of a trip. they have traveled 80 miles. how far is the trip?

a. 32 miles c. 200 miles
b. 40 miles d. 20 miles
use for #6-8: priya runs 8 laps around a track in 12 minutes.

1. how many minutes per lap is that?
2. how many laps per minute is that?
3. at that rate, how long does it take priya to run 18 laps?

Explanation:

Question 1

Step1: Calculate the ratio of chocolate candies to total candies

To find the percentage, we first find the fraction of chocolate candies. The number of chocolate candies is 12, and the total number of candies is 18. So the fraction is $\frac{12}{18}$.

Step2: Simplify the fraction and convert to percentage

Simplify $\frac{12}{18}=\frac{2}{3}\approx0.67$. To convert this to a percentage, we multiply by 100, so $0.67\times100 = 67\%$.

To determine which trips take 4 hours, we use the formula $time=\frac{distance}{speed}$.

• For option A: Distance = 0.5 miles, Speed = 4 miles per hour. Time = $\frac{0.5}{4}=0.125$ hours (not 4 hours).
• For option B: Distance = 256 miles, Speed = 64 miles per hour. Time = $\frac{256}{64}=4$ hours (this trip takes 4 hours).
• For option C: Distance = 220 miles, Speed = 55 miles per hour. Time = $\frac{220}{55}=4$ hours (this trip takes 4 hours).

Step1: Let the total distance of the trip be $x$ miles.

We know that 40% of $x$ is 80 miles. In equation form, this is $0.4x = 80$.

Step2: Solve for $x$

To find $x$, we divide both sides of the equation by 0.4: $x=\frac{80}{0.4}=200$ miles.

Answer:

D. 67%

Question 2 - 4