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Answer :
To solve the problem, we need to determine which equation best represents Kiran's budget for the gathering, taking into account the amounts of sparkling water and pretzels needed and their costs.
Here's how we can approach the problem:
1. Calculate Total Amount Needed:
- Each person will consume 12 ounces of sparkling water and 3 ounces of pretzels.
- Since there are 10 people (including Kiran's family), we multiply these amounts by 10:
- 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]
2. Determine the Number of Bottles and Packages Required:
- Each bottle of sparkling water contains 22 ounces, so we divide the total ounces needed by 22 to find the number of bottles:
- Bottles needed: [tex]\(\frac{120 \text{ ounces}}{22 \text{ ounces/bottle}} \approx 5.45\)[/tex]
- This means 6 bottles are needed (since you can't buy a fraction of a bottle).
- Each package of pretzels contains 16 ounces, so we divide the total ounces needed by 16 to find the number of packages:
- Packages needed: [tex]\(\frac{30 \text{ ounces}}{16 \text{ ounces/package}} \approx 1.875\)[/tex]
- This means 2 packages are needed (rounding up for the same reason as above).
3. Calculate the Cost:
- The cost of each bottle of sparkling water is [tex]$1.50, so the total cost for bottles is:
- \(6 \times \text{\$[/tex]1.50} = \[tex]$9.00\)
- The cost of each package of pretzels is $[/tex]2.99, so the total cost for packages is:
- [tex]\(2 \times \text{\$2.99} = \$5.98\)[/tex]
4. Total Budget:
- Adding the costs for bottles and packages gives us the total budget:
- Total budget [tex]\(= \$9.00 + \$5.98 = \$14.98\)[/tex]
Now, let's look at the given options:
a) [tex]\(12s + 3p = b\)[/tex]
b) [tex]\(12 \cdot 10 + 3 \cdot 10 = b\)[/tex]
c) [tex]\(1.50s + 2.99p = b\)[/tex]
d) [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
The correct equation that matches our total budget calculation is:
d) [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
This equation correctly matches the total cost calculation of $14.98 for six bottles of sparkling water and two packages of pretzels.
Here's how we can approach the problem:
1. Calculate Total Amount Needed:
- Each person will consume 12 ounces of sparkling water and 3 ounces of pretzels.
- Since there are 10 people (including Kiran's family), we multiply these amounts by 10:
- 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]
2. Determine the Number of Bottles and Packages Required:
- Each bottle of sparkling water contains 22 ounces, so we divide the total ounces needed by 22 to find the number of bottles:
- Bottles needed: [tex]\(\frac{120 \text{ ounces}}{22 \text{ ounces/bottle}} \approx 5.45\)[/tex]
- This means 6 bottles are needed (since you can't buy a fraction of a bottle).
- Each package of pretzels contains 16 ounces, so we divide the total ounces needed by 16 to find the number of packages:
- Packages needed: [tex]\(\frac{30 \text{ ounces}}{16 \text{ ounces/package}} \approx 1.875\)[/tex]
- This means 2 packages are needed (rounding up for the same reason as above).
3. Calculate the Cost:
- The cost of each bottle of sparkling water is [tex]$1.50, so the total cost for bottles is:
- \(6 \times \text{\$[/tex]1.50} = \[tex]$9.00\)
- The cost of each package of pretzels is $[/tex]2.99, so the total cost for packages is:
- [tex]\(2 \times \text{\$2.99} = \$5.98\)[/tex]
4. Total Budget:
- Adding the costs for bottles and packages gives us the total budget:
- Total budget [tex]\(= \$9.00 + \$5.98 = \$14.98\)[/tex]
Now, let's look at the given options:
a) [tex]\(12s + 3p = b\)[/tex]
b) [tex]\(12 \cdot 10 + 3 \cdot 10 = b\)[/tex]
c) [tex]\(1.50s + 2.99p = b\)[/tex]
d) [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
The correct equation that matches our total budget calculation is:
d) [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]
This equation correctly matches the total cost calculation of $14.98 for six bottles of sparkling water and two packages of pretzels.
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