Answer :
To solve this problem, we need to figure out the total cost for sparkling water and pretzels for Kiran's football gathering. Let's break it down step by step:
1. Determine the total amounts needed:
- There are 10 people attending the gathering.
- Each person will consume 12 ounces of sparkling water and 3 ounces of pretzels.
2. Calculate the total quantities required:
- For sparkling water:
[tex]\[
12 \, \text{ounces per person} \times 10 \, \text{people} = 120 \, \text{ounces of sparkling water}
\][/tex]
- For pretzels:
[tex]\[
3 \, \text{ounces per person} \times 10 \, \text{people} = 30 \, \text{ounces of pretzels}
\][/tex]
3. Determine how many bottles and packages are needed:
- Each bottle of sparkling water is 22 ounces.
- Each package of pretzels is 16 ounces.
- The number of sparkling water bottles needed:
[tex]\[
\frac{120 \, \text{ounces needed}}{22 \, \text{ounces per bottle}} \approx 5.45 \, \text{bottles}
\][/tex]
- The number of pretzel packages needed:
[tex]\[
\frac{30 \, \text{ounces needed}}{16 \, \text{ounces per package}} \approx 1.875 \, \text{packages}
\][/tex]
4. Calculate the total costs:
- Each bottle of sparkling water costs [tex]$1.50.
- Each package of pretzels costs $[/tex]2.99.
- The cost for the sparkling water:
[tex]\[
5.45 \, \text{bottles} \times \$1.50 \, \text{per bottle} = \approx \$8.18
\][/tex]
- The cost for the pretzels:
[tex]\[
1.875 \, \text{packages} \times \$2.99 \, \text{per package} = \approx \$5.61
\][/tex]
5. Combine the costs for the total budget:
- Total budget:
[tex]\[
\$8.18 + \$5.61 = \approx \$13.79
\][/tex]
From these calculations, the correct equation that represents Kiran's budget, considering the total cost in dollars, is when both the number of bottles and the number of packages are multiplied by their respective costs, option D) [tex]$1.50 \cdot 6 + 2.99 \cdot 2 = b$[/tex] would provide an estimation closest to this value. However, since we more accurately calculated these, the precise total budget is approximately \$13.79, reflecting the values used.
1. Determine the total amounts needed:
- There are 10 people attending the gathering.
- Each person will consume 12 ounces of sparkling water and 3 ounces of pretzels.
2. Calculate the total quantities required:
- For sparkling water:
[tex]\[
12 \, \text{ounces per person} \times 10 \, \text{people} = 120 \, \text{ounces of sparkling water}
\][/tex]
- For pretzels:
[tex]\[
3 \, \text{ounces per person} \times 10 \, \text{people} = 30 \, \text{ounces of pretzels}
\][/tex]
3. Determine how many bottles and packages are needed:
- Each bottle of sparkling water is 22 ounces.
- Each package of pretzels is 16 ounces.
- The number of sparkling water bottles needed:
[tex]\[
\frac{120 \, \text{ounces needed}}{22 \, \text{ounces per bottle}} \approx 5.45 \, \text{bottles}
\][/tex]
- The number of pretzel packages needed:
[tex]\[
\frac{30 \, \text{ounces needed}}{16 \, \text{ounces per package}} \approx 1.875 \, \text{packages}
\][/tex]
4. Calculate the total costs:
- Each bottle of sparkling water costs [tex]$1.50.
- Each package of pretzels costs $[/tex]2.99.
- The cost for the sparkling water:
[tex]\[
5.45 \, \text{bottles} \times \$1.50 \, \text{per bottle} = \approx \$8.18
\][/tex]
- The cost for the pretzels:
[tex]\[
1.875 \, \text{packages} \times \$2.99 \, \text{per package} = \approx \$5.61
\][/tex]
5. Combine the costs for the total budget:
- Total budget:
[tex]\[
\$8.18 + \$5.61 = \approx \$13.79
\][/tex]
From these calculations, the correct equation that represents Kiran's budget, considering the total cost in dollars, is when both the number of bottles and the number of packages are multiplied by their respective costs, option D) [tex]$1.50 \cdot 6 + 2.99 \cdot 2 = b$[/tex] would provide an estimation closest to this value. However, since we more accurately calculated these, the precise total budget is approximately \$13.79, reflecting the values used.
