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Answer :
Sure! Let's go through the problem step-by-step.
Question Recap:
Kiran's family is hosting a football gathering for 10 people. They will serve sparkling water and pretzels. Each person gets 12 ounces of sparkling water and 3 ounces of pretzels.
The costs are:
- A bottle of sparkling water (22 ounces) costs [tex]$1.50.
- A package of pretzels (16 ounces) costs $[/tex]2.99.
We need to find which equation best represents Kiran's budget using the information provided.
Step 1: Calculate total consumption per person
- For sparkling water: 12 ounces per person.
- For pretzels: 3 ounces per person.
Step 2: Calculate the total consumption for the gathering
- Total sparkling water needed: [tex]\(12 \text{ ounces/person} \times 10 \text{ people} = 120 \text{ ounces}\)[/tex].
- Total pretzels needed: [tex]\(3 \text{ ounces/person} \times 10 \text{ people} = 30 \text{ ounces}\)[/tex].
Step 3: Calculate the number of bottles and packages needed
- Number of bottles of sparkling water: [tex]\(\frac{120 \text{ ounces}}{22 \text{ ounces/bottle}} \approx 5.45 \text{ bottles}\)[/tex].
- Number of packages of pretzels: [tex]\(\frac{30 \text{ ounces}}{16 \text{ ounces/package}} \approx 1.88 \text{ packages}\)[/tex].
Step 4: Calculate the total cost
- Cost of sparkling water: [tex]\(5.45 \text{ bottles} \times \$1.50 \approx \$8.18\)[/tex].
- Cost of pretzels: [tex]\(1.88 \text{ packages} \times \$2.99 \approx \$5.63\)[/tex].
- Total cost: \[tex]$8.18 + \$[/tex]5.63 = \$13.81 (rounding may cause small discrepancies).
Choosing the Correct Equation:
1. Option A: [tex]\(12s + 3p = b\)[/tex]
- This is not appropriate since it does not incorporate the number of people nor the costs.
2. Option B: [tex]\(12 \cdot 10 + 3 \cdot 10 = b\)[/tex]
- This correctly calculates total ounces consumed: [tex]\(12 \cdot 10 + 3 \cdot 10 = 120 + 30 = 150\)[/tex].
3. Option C: [tex]\(1.50s + 2.99p = b\)[/tex]
- This is incorrect because it incorrectly tries to use the prices directly on the quantity of ounces which is not logical.
4. Option D: [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
- This accounts for the proportional use of bottles and packages (about 6 bottles and 2 packages), costing approximately [tex]\( 1.50 \cdot 6 + 2.99 \cdot 2 = 9 + 5.98 = 14.98 \)[/tex].
Hence, the correct breakdown and representation for Kiran's budget based on the food costs is:
Option D: [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
Question Recap:
Kiran's family is hosting a football gathering for 10 people. They will serve sparkling water and pretzels. Each person gets 12 ounces of sparkling water and 3 ounces of pretzels.
The costs are:
- A bottle of sparkling water (22 ounces) costs [tex]$1.50.
- A package of pretzels (16 ounces) costs $[/tex]2.99.
We need to find which equation best represents Kiran's budget using the information provided.
Step 1: Calculate total consumption per person
- For sparkling water: 12 ounces per person.
- For pretzels: 3 ounces per person.
Step 2: Calculate the total consumption for the gathering
- Total sparkling water needed: [tex]\(12 \text{ ounces/person} \times 10 \text{ people} = 120 \text{ ounces}\)[/tex].
- Total pretzels needed: [tex]\(3 \text{ ounces/person} \times 10 \text{ people} = 30 \text{ ounces}\)[/tex].
Step 3: Calculate the number of bottles and packages needed
- Number of bottles of sparkling water: [tex]\(\frac{120 \text{ ounces}}{22 \text{ ounces/bottle}} \approx 5.45 \text{ bottles}\)[/tex].
- Number of packages of pretzels: [tex]\(\frac{30 \text{ ounces}}{16 \text{ ounces/package}} \approx 1.88 \text{ packages}\)[/tex].
Step 4: Calculate the total cost
- Cost of sparkling water: [tex]\(5.45 \text{ bottles} \times \$1.50 \approx \$8.18\)[/tex].
- Cost of pretzels: [tex]\(1.88 \text{ packages} \times \$2.99 \approx \$5.63\)[/tex].
- Total cost: \[tex]$8.18 + \$[/tex]5.63 = \$13.81 (rounding may cause small discrepancies).
Choosing the Correct Equation:
1. Option A: [tex]\(12s + 3p = b\)[/tex]
- This is not appropriate since it does not incorporate the number of people nor the costs.
2. Option B: [tex]\(12 \cdot 10 + 3 \cdot 10 = b\)[/tex]
- This correctly calculates total ounces consumed: [tex]\(12 \cdot 10 + 3 \cdot 10 = 120 + 30 = 150\)[/tex].
3. Option C: [tex]\(1.50s + 2.99p = b\)[/tex]
- This is incorrect because it incorrectly tries to use the prices directly on the quantity of ounces which is not logical.
4. Option D: [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
- This accounts for the proportional use of bottles and packages (about 6 bottles and 2 packages), costing approximately [tex]\( 1.50 \cdot 6 + 2.99 \cdot 2 = 9 + 5.98 = 14.98 \)[/tex].
Hence, the correct breakdown and representation for Kiran's budget based on the food costs is:
Option D: [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
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