Answer :
Sure! Let's go through each problem one by one to see if the two rates form a proportion.
5. 55 miles in 1 hour; 450 miles in 8 hours
- Calculate the rate for each condition:
- First rate: 55 miles in 1 hour is 55 miles/hour.
- Second rate: 450 miles in 8 hours is 450 ÷ 8 = 56.25 miles/hour.
Since 55 does not equal 56.25, these rates do not form a proportion.
6. [tex]$3.00 for 32 ounces of strawberries; $[/tex]1.75 for 24 ounces of strawberries
- Calculate the rate for each condition:
- First rate: [tex]$3.00 for 32 ounces is 3.00 ÷ 32 = $[/tex]0.09375 per ounce.
- Second rate: [tex]$1.75 for 24 ounces is 1.75 ÷ 24 = $[/tex]0.072916...
Since [tex]$0.09375 does not equal $[/tex]0.072916..., these rates do not form a proportion.
7. 45 baskets in 85 shots; 54 baskets in 102 shots
- Calculate the rate for each condition:
- First rate: 45 baskets in 85 shots is 45 ÷ 85 = 0.5294...
- Second rate: 54 baskets in 102 shots is 54 ÷ 102 = 0.5294...
Since the rates are equal, these rates form a proportion.
8. 18 push-ups in 60 seconds; 27 push-ups in 90 seconds
- Calculate the rate for each condition:
- First rate: 18 push-ups in 60 seconds is 18 ÷ 60 = 0.3 push-ups per second.
- Second rate: 27 push-ups in 90 seconds is 27 ÷ 90 = 0.3 push-ups per second.
Since the rates are equal, these rates form a proportion.
9. 2 grams of protein per 1-cup serving; 1 gram of protein per half-cup serving
- Calculate the rate for each condition:
- First rate: 2 grams per 1 cup is 2 grams/cup.
- Second rate: 1 gram per half-cup is 1 ÷ 0.5 = 2 grams/cup.
Since the rates are equal, these rates form a proportion.
10. A 50-fluid-ounce bottle of laundry detergent washes 32 loads; a 100-fluid-ounce bottle washes 60 loads
- Calculate the rate for each condition:
- First rate: 50 fluid ounces for 32 loads is 50 ÷ 32 ≈ 1.5625 fluid ounces per load.
- Second rate: 100 fluid ounces for 60 loads is 100 ÷ 60 ≈ 1.6667 fluid ounces per load.
Since 1.5625 does not equal 1.6667, these rates do not form a proportion.
In summary:
- Proportions are formed in problems 7, 8, and 9.
- No proportions in problems 5, 6, and 10.
5. 55 miles in 1 hour; 450 miles in 8 hours
- Calculate the rate for each condition:
- First rate: 55 miles in 1 hour is 55 miles/hour.
- Second rate: 450 miles in 8 hours is 450 ÷ 8 = 56.25 miles/hour.
Since 55 does not equal 56.25, these rates do not form a proportion.
6. [tex]$3.00 for 32 ounces of strawberries; $[/tex]1.75 for 24 ounces of strawberries
- Calculate the rate for each condition:
- First rate: [tex]$3.00 for 32 ounces is 3.00 ÷ 32 = $[/tex]0.09375 per ounce.
- Second rate: [tex]$1.75 for 24 ounces is 1.75 ÷ 24 = $[/tex]0.072916...
Since [tex]$0.09375 does not equal $[/tex]0.072916..., these rates do not form a proportion.
7. 45 baskets in 85 shots; 54 baskets in 102 shots
- Calculate the rate for each condition:
- First rate: 45 baskets in 85 shots is 45 ÷ 85 = 0.5294...
- Second rate: 54 baskets in 102 shots is 54 ÷ 102 = 0.5294...
Since the rates are equal, these rates form a proportion.
8. 18 push-ups in 60 seconds; 27 push-ups in 90 seconds
- Calculate the rate for each condition:
- First rate: 18 push-ups in 60 seconds is 18 ÷ 60 = 0.3 push-ups per second.
- Second rate: 27 push-ups in 90 seconds is 27 ÷ 90 = 0.3 push-ups per second.
Since the rates are equal, these rates form a proportion.
9. 2 grams of protein per 1-cup serving; 1 gram of protein per half-cup serving
- Calculate the rate for each condition:
- First rate: 2 grams per 1 cup is 2 grams/cup.
- Second rate: 1 gram per half-cup is 1 ÷ 0.5 = 2 grams/cup.
Since the rates are equal, these rates form a proportion.
10. A 50-fluid-ounce bottle of laundry detergent washes 32 loads; a 100-fluid-ounce bottle washes 60 loads
- Calculate the rate for each condition:
- First rate: 50 fluid ounces for 32 loads is 50 ÷ 32 ≈ 1.5625 fluid ounces per load.
- Second rate: 100 fluid ounces for 60 loads is 100 ÷ 60 ≈ 1.6667 fluid ounces per load.
Since 1.5625 does not equal 1.6667, these rates do not form a proportion.
In summary:
- Proportions are formed in problems 7, 8, and 9.
- No proportions in problems 5, 6, and 10.
