Question

name:
7-3 additional practice

1. edith and rashida are shooting free throws. complete the ratio tables. who has a better ratio of baskets to shots?

edith
baskets 1 　 　 4 5
shots 3 6 9
rashida
baskets 2 　 　 8 10
shots 5 10 15

1. in mrs. washington’s class, there are 2 students in band for every 3 students in chorus. in mr. utley’s class there are 5 students in band for every 7 students in chorus. complete the ratio tables. which class has a greater ratio of students in band to students in chorus?

mrs.washington’s class
band 2
chorus 3
mr. utley’s class
band 5
chorus 7

Explanation:

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Problem 1

Edith's Ratio Table

Step1: Find scaling factor

Edith's base ratio: $\frac{\text{Baskets}}{\text{Shots}} = \frac{1}{3}$

Step2: Calculate baskets for 6 shots

Scaling factor: $\frac{6}{3}=2$
Baskets: $1 \times 2 = 2$

Step3: Calculate baskets for 9 shots

Scaling factor: $\frac{9}{3}=3$
Baskets: $1 \times 3 = 3$

Step4: Calculate shots for 4 baskets

Scaling factor: $\frac{4}{1}=4$
Shots: $3 \times 4 = 12$

Step5: Calculate shots for 5 baskets

Scaling factor: $\frac{5}{1}=5$
Shots: $3 \times 5 = 15$

Step6: Find Edith's success rate

Rate: $\frac{1}{3} \approx 0.333$

Rashida's Ratio Table

Step1: Find scaling factor

Rashida's base ratio: $\frac{\text{Baskets}}{\text{Shots}} = \frac{2}{5}$

Step2: Calculate baskets for 10 shots

Scaling factor: $\frac{10}{5}=2$
Baskets: $2 \times 2 = 4$

Step3: Calculate baskets for 15 shots

Scaling factor: $\frac{15}{5}=3$
Baskets: $2 \times 3 = 6$

Step4: Calculate shots for 8 baskets

Scaling factor: $\frac{8}{2}=4$
Shots: $5 \times 4 = 20$

Step5: Calculate shots for 10 baskets

Scaling factor: $\frac{10}{2}=5$
Shots: $5 \times 5 = 25$

Step6: Find Rashida's success rate

Rate: $\frac{2}{5} = 0.4$

Step7: Compare the two rates

$0.4 > 0.333$, so Rashida's ratio is better.

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Problem 2

Mrs. Washington's Class

Step1: Find scaling factor

Base ratio: $\frac{\text{Band}}{\text{Chorus}} = \frac{2}{3}$

Step2: Scale by 2

Band: $2 \times 2 = 4$, Chorus: $3 \times 2 = 6$

Step3: Scale by 3

Band: $2 \times 3 = 6$, Chorus: $3 \times 3 = 9$

Step4: Scale by 4

Band: $2 \times 4 = 8$, Chorus: $3 \times 4 = 12$

Step5: Scale by 5

Band: $2 \times 5 = 10$, Chorus: $3 \times 5 = 15$

Step6: Find the ratio value

Rate: $\frac{2}{3} \approx 0.667$

Mr. Utley's Class

Step1: Find scaling factor

Base ratio: $\frac{\text{Band}}{\text{Chorus}} = \frac{5}{7}$

Step2: Scale by 2

Band: $5 \times 2 = 10$, Chorus: $7 \times 2 = 14$

Step3: Scale by 3

Band: $5 \times 3 = 15$, Chorus: $7 \times 3 = 21$

Step4: Scale by 4

Band: $5 \times 4 = 20$, Chorus: $7 \times 4 = 28$

Step5: Scale by 5

Band: $5 \times 5 = 25$, Chorus: $7 \times 5 = 35$

Step6: Find the ratio value

Rate: $\frac{5}{7} \approx 0.714$

Step7: Compare the two rates

$0.714 > 0.667$, so Mr. Utley's class has a greater ratio.

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Answer:

1. Completed tables:

• Edith: Baskets = [1, 2, 3, 4, 5]; Shots = [3, 6, 9, 12, 15]
• Rashida: Baskets = [2, 4, 6, 8, 10]; Shots = [5, 10, 15, 20, 25]
• Rashida has a better ratio of baskets to shots.

1. Completed tables:

• Mrs. Washington's Class: Band = [2, 4, 6, 8, 10]; Chorus = [3, 6, 9, 12, 15]
• Mr. Utley's Class: Band = [5, 10, 15, 20, 25]; Chorus = [7, 14, 21, 28, 35]
• Mr. Utley's class has a greater ratio of band to chorus students.