Question

name: jordan king
date:
per: 8
unit 4: ratio, proportion, & percent
homework 2: rates & unit rates
directions: express each rate as a unit rate.

1. 108 pencils to 27 students
2. 450 calories in 6 cupcakes
3. 21 hot dogs eaten in 60 seconds
4. 5 points scored in 4 quarters
5. 9 inches of snow in 15 hours
6. 378 miles to 15 gallons of gas
7. 1\frac{1}{2} cups of sugar for every \frac{2}{3} cup of flour
8. 28\frac{1}{3} minutes to run 3\frac{1}{3} miles
9. the table below shows the amount of time in minutes it took to drain four different tanks. which tank drained the fastest per minute?

tank	capacity (gal)	time (m)
b	64	18
c	96	28
d	50	16

1. karen walked three miles in 48 minutes. bob walked one mile further than karen. if it took bob 1 hour and 5 minutes to complete his walk, who walked at a faster rate?

directions: express each rate as a unit rate. round to the nearest cent if necessary.

1. six tubs of frosting for $5
2. $7.90 for 50 ounces of laundry soap
3. 24 water bottles for $2.95
4. $200 for 12 piano lessons
5. $14.40 for 4.5 pounds of beef
6. 2\frac{3}{4} yards of fabric for $22

directions: determine whether option a or option b is the better deal.
17.
option a: $9.95 for 30 oz. of coffee
option b: $3.50 for 12 oz. of coffee
18.
option a: 40 trash bags for $6.29
option b: 24 trash bags for $3.89

Explanation:

Step1: Find unit rate for Q1

$\frac{108}{27} = 4$ pencils/student

Step2: Find unit rate for Q2

$\frac{450}{6} = 75$ calories/cupcake

Step3: Find unit rate for Q3

$\frac{21}{60} = 0.35$ hot dogs/second

Step4: Find unit rate for Q4

$\frac{5}{4} = 1.25$ points/quarter

Step5: Find unit rate for Q5

$\frac{9}{15} = 0.6$ inches/hour

Step6: Find unit rate for Q6

$\frac{378}{15} = 25.2$ miles/gallon

Step7: Convert mixed numbers, find unit rate for Q7

$1\frac{1}{2}=\frac{3}{2}$, $\frac{\frac{3}{2}}{\frac{2}{3}}=\frac{3}{2}\times\frac{3}{2}=\frac{9}{4}=2.25$ cups sugar/cup flour

Step8: Convert mixed numbers, find unit rate for Q8

$28\frac{1}{3}=\frac{85}{3}$, $3\frac{1}{3}=\frac{10}{3}$, $\frac{\frac{85}{3}}{\frac{10}{3}}=8.5$ minutes/mile

Step9: Calculate drain rate for each tank

Tank A: $\frac{80}{24}\approx3.33$ gal/min; Tank B: $\frac{64}{18}\approx3.56$ gal/min; Tank C: $\frac{96}{28}\approx3.43$ gal/min; Tank D: $\frac{50}{16}=3.125$ gal/min. Compare values.

Step10: Calculate walking rates

Karen: $\frac{3}{48}=0.0625$ miles/min; Bob: 4 miles in 65 min, $\frac{4}{65}\approx0.0615$ miles/min. Compare values.

Step11: Find unit rate for Q11

$\frac{5}{6}\approx\$0.83$ per tub

Step12: Find unit rate for Q12

$\frac{7.90}{50}=\$0.16$ per ounce

Step13: Find unit rate for Q13

$\frac{2.95}{24}\approx\$0.12$ per bottle

Step14: Find unit rate for Q14

$\frac{200}{12}\approx\$16.67$ per lesson

Step15: Verify unit rate for Q15

$\frac{14.40}{4.5}=\$3.20$ per pound

Step16: Convert mixed number, find unit rate for Q16

$2\frac{3}{4}=\frac{11}{4}$, $\frac{22}{\frac{11}{4}}=22\times\frac{4}{11}=\$8$ per yard

Step17: Find unit price for coffee

Option A: $\frac{9.95}{30}\approx\$0.33$ per oz; Option B: $\frac{3.50}{12}\approx\$0.29$ per oz. Compare values.

Step18: Find unit price for trash bags

Option A: $\frac{6.29}{40}\approx\$0.16$ per bag; Option B: $\frac{3.89}{24}\approx\$0.16$ per bag (rounded). Compare values.

Answer:

1. 4 pencils per student
2. 75 calories per cupcake
3. 0.35 hot dogs per second
4. 1.25 points per quarter
5. 0.6 inches of snow per hour
6. 25.2 miles per gallon
7. 2.25 cups of sugar per cup of flour
8. 8.5 minutes per mile
9. Tank B
10. Karen
11. $\$0.83$ per tub of frosting
12. $\$0.16$ per ounce of laundry soap
13. $\$0.12$ per water bottle
14. $\$16.67$ per piano lesson
15. $\$3.20$ per pound of beef
16. $\$8$ per yard of fabric
17. Option B: $\$3.50$ for 12 oz. of coffee
18. Option B: 24 trash bags for $\$3.89$ (lower unit cost when unrounded: $\$0.162$ vs $\$0.158$)