Answer :
To find the correct equation that represents Kiran's budget for the gathering, let's break down the problem step-by-step:
1. Determine the Total Amount of Sparkling Water and Pretzels Needed:
- Kiran's family will have 10 people at the gathering.
- Each person will require 12 ounces of sparkling water and 3 ounces of pretzels.
Therefore:
- Total ounces of sparkling water needed = [tex]\( 12 \, \text{ounces/person} \times 10 \, \text{people} = 120 \, \text{ounces} \)[/tex]
- Total ounces of pretzels needed = [tex]\( 3 \, \text{ounces/person} \times 10 \, \text{people} = 30 \, \text{ounces} \)[/tex]
2. Calculate the Number of Sparkling Water Bottles Needed:
- Each bottle of sparkling water contains 22 ounces.
- To find out how many bottles are needed, divide the total ounces required by the ounces per bottle: [tex]\( \frac{120 \, \text{ounces}}{22 \, \text{ounces per bottle}} \approx 5.45 \)[/tex]
- Since you can't buy a fraction of a bottle, you'll need to round up to 6 bottles.
3. Calculate the Cost for Sparkling Water:
- Each bottle costs \[tex]$1.50.
- Total cost for sparkling water = \( 6 \, \text{bottles} \times \$[/tex]1.50/\text{bottle} = \[tex]$9.00 \)
4. Calculate the Number of Pretzel Packages Needed:
- Each package of pretzels contains 16 ounces.
- To find out how many packages are needed, divide the total ounces required by the ounces per package: \( \frac{30 \, \text{ounces}}{16 \, \text{ounces per package}} \approx 1.875 \)
- You need to round up, so you'll require 2 packages.
5. Calculate the Cost for Pretzels:
- Each package costs \$[/tex]2.99.
- Total cost for pretzels = [tex]\( 2 \, \text{packages} \times \$2.99/\text{package} = \$5.98 \)[/tex]
6. Calculate the Total Budget:
- Total budget required (b) = Cost for sparkling water + Cost for pretzels
- Total budget = [tex]\( \$9.00 + \$5.98 = \$14.98 \)[/tex]
Considering all the calculations, the correct equation that represents Kiran's budget is option D: [tex]\( 1.50 \cdot 6 + 2.99 \cdot 2 = b \)[/tex].
1. Determine the Total Amount of Sparkling Water and Pretzels Needed:
- Kiran's family will have 10 people at the gathering.
- Each person will require 12 ounces of sparkling water and 3 ounces of pretzels.
Therefore:
- Total ounces of sparkling water needed = [tex]\( 12 \, \text{ounces/person} \times 10 \, \text{people} = 120 \, \text{ounces} \)[/tex]
- Total ounces of pretzels needed = [tex]\( 3 \, \text{ounces/person} \times 10 \, \text{people} = 30 \, \text{ounces} \)[/tex]
2. Calculate the Number of Sparkling Water Bottles Needed:
- Each bottle of sparkling water contains 22 ounces.
- To find out how many bottles are needed, divide the total ounces required by the ounces per bottle: [tex]\( \frac{120 \, \text{ounces}}{22 \, \text{ounces per bottle}} \approx 5.45 \)[/tex]
- Since you can't buy a fraction of a bottle, you'll need to round up to 6 bottles.
3. Calculate the Cost for Sparkling Water:
- Each bottle costs \[tex]$1.50.
- Total cost for sparkling water = \( 6 \, \text{bottles} \times \$[/tex]1.50/\text{bottle} = \[tex]$9.00 \)
4. Calculate the Number of Pretzel Packages Needed:
- Each package of pretzels contains 16 ounces.
- To find out how many packages are needed, divide the total ounces required by the ounces per package: \( \frac{30 \, \text{ounces}}{16 \, \text{ounces per package}} \approx 1.875 \)
- You need to round up, so you'll require 2 packages.
5. Calculate the Cost for Pretzels:
- Each package costs \$[/tex]2.99.
- Total cost for pretzels = [tex]\( 2 \, \text{packages} \times \$2.99/\text{package} = \$5.98 \)[/tex]
6. Calculate the Total Budget:
- Total budget required (b) = Cost for sparkling water + Cost for pretzels
- Total budget = [tex]\( \$9.00 + \$5.98 = \$14.98 \)[/tex]
Considering all the calculations, the correct equation that represents Kiran's budget is option D: [tex]\( 1.50 \cdot 6 + 2.99 \cdot 2 = b \)[/tex].
