Answer :
Sure! Let's break down the problem and find out which equation best represents Kiran's budget for the football gathering. We know the following details:
1. Number of people: Including Kiran's family, there will be 10 people.
2. Sparkling water: Each person will have 12 ounces.
3. Pretzels: Each person will have [tex]\(\sqrt{3}\)[/tex] ounces.
4. Sparkling water bottles: Each bottle contains 22 ounces and costs \[tex]$1.50.
5. Pretzel packages: Each package contains 16 ounces and costs \$[/tex]2.99.
Now, let's go through each step to solve the problem:
### Step 1: Calculate Total Ounces Needed
- Sparkling Water:
[tex]\[
\text{Total Sparkling Water} = 12 \, \text{ounces/person} \times 10 \, \text{people} = 120 \, \text{ounces}
\][/tex]
- Pretzels:
[tex]\[
\text{Total Pretzels} = \sqrt{3} \, \text{ounces/person} \times 10 \, \text{people} \approx 17.32 \, \text{ounces}
\][/tex]
### Step 2: Calculate Number of Bottles and Packages Needed
- Bottles of Sparkling Water Needed:
[tex]\[
\text{Bottles Needed} = \lceil \frac{120 \, \text{ounces}}{22 \, \text{ounces/bottle}} \rceil = 6 \, \text{bottles}
\][/tex]
- Packages of Pretzels Needed:
[tex]\[
\text{Packages Needed} = \lceil \frac{17.32 \, \text{ounces}}{16 \, \text{ounces/package}} \rceil = 2 \, \text{packages}
\][/tex]
### Step 3: Calculate Total Cost
- Cost of Sparkling Water:
[tex]\[
\text{Total Cost of Sparkling Water} = 6 \, \text{bottles} \times \$1.50/\text{bottle} = \$9.00
\][/tex]
- Cost of Pretzels:
[tex]\[
\text{Total Cost of Pretzels} = 2 \, \text{packages} \times \$2.99/\text{package} = \$5.98
\][/tex]
### Step 4: Calculate Total Budget
- Total Budget:
[tex]\[
\text{Total Budget} = \$9.00 + \$5.98 = \$14.98
\][/tex]
### Conclusion
After calculating, the best equation representing Kiran's budget is based on the total ounces and costs needed. In this case, the choice that aligns best with our steps and the calculated budget is:
- Option D: [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex] which results in [tex]\(b = 14.98\)[/tex], aligning with our calculated total budget.
1. Number of people: Including Kiran's family, there will be 10 people.
2. Sparkling water: Each person will have 12 ounces.
3. Pretzels: Each person will have [tex]\(\sqrt{3}\)[/tex] ounces.
4. Sparkling water bottles: Each bottle contains 22 ounces and costs \[tex]$1.50.
5. Pretzel packages: Each package contains 16 ounces and costs \$[/tex]2.99.
Now, let's go through each step to solve the problem:
### Step 1: Calculate Total Ounces Needed
- Sparkling Water:
[tex]\[
\text{Total Sparkling Water} = 12 \, \text{ounces/person} \times 10 \, \text{people} = 120 \, \text{ounces}
\][/tex]
- Pretzels:
[tex]\[
\text{Total Pretzels} = \sqrt{3} \, \text{ounces/person} \times 10 \, \text{people} \approx 17.32 \, \text{ounces}
\][/tex]
### Step 2: Calculate Number of Bottles and Packages Needed
- Bottles of Sparkling Water Needed:
[tex]\[
\text{Bottles Needed} = \lceil \frac{120 \, \text{ounces}}{22 \, \text{ounces/bottle}} \rceil = 6 \, \text{bottles}
\][/tex]
- Packages of Pretzels Needed:
[tex]\[
\text{Packages Needed} = \lceil \frac{17.32 \, \text{ounces}}{16 \, \text{ounces/package}} \rceil = 2 \, \text{packages}
\][/tex]
### Step 3: Calculate Total Cost
- Cost of Sparkling Water:
[tex]\[
\text{Total Cost of Sparkling Water} = 6 \, \text{bottles} \times \$1.50/\text{bottle} = \$9.00
\][/tex]
- Cost of Pretzels:
[tex]\[
\text{Total Cost of Pretzels} = 2 \, \text{packages} \times \$2.99/\text{package} = \$5.98
\][/tex]
### Step 4: Calculate Total Budget
- Total Budget:
[tex]\[
\text{Total Budget} = \$9.00 + \$5.98 = \$14.98
\][/tex]
### Conclusion
After calculating, the best equation representing Kiran's budget is based on the total ounces and costs needed. In this case, the choice that aligns best with our steps and the calculated budget is:
- Option D: [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex] which results in [tex]\(b = 14.98\)[/tex], aligning with our calculated total budget.
