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Kiran's family is having people over to watch a football game. They plan to serve sparkling water and pretzels. They are preparing 12 ounces of sparkling water and 3 ounces of pretzels per person. Including Kiran's family, there will be 10 people at the gathering.

A bottle of sparkling water contains 22 ounces and costs [tex]$\$1.50$[/tex]. A package of pretzels contains 16 ounces and costs [tex]$\$2.99$[/tex]. Let [tex]$n$[/tex] represent the number of people watching the football game, [tex]$s$[/tex] represent the ounces of sparkling water, [tex]$p$[/tex] represent the ounces of pretzels, and [tex]$b$[/tex] represent Kiran's budget in dollars. Which equation best represents Kiran's budget?

Select the correct choice.

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]

Answer :

Sure, let's break down the problem step by step to understand how to find the correct equation for Kiran's budget.

1. Determine the total amount needed per person:
- Each person will consume 12 ounces of sparkling water.
- Each person will consume 3 ounces of pretzels.
- There are 10 people in total (including Kiran's family).

2. Calculate the total quantity needed for the entire group:
- For sparkling water: [tex]\( 12 \text{ ounces/person} \times 10 \text{ people} = 120 \text{ ounces} \)[/tex]
- For pretzels: [tex]\( 3 \text{ ounces/person} \times 10 \text{ people} = 30 \text{ ounces} \)[/tex]

3. Determine how many units of each product need to be purchased:
- A bottle of sparkling water contains 22 ounces.
- The total sparkling water needed is 120 ounces. To find the number of bottles needed:
[tex]\[
\text{Bottles needed} = \frac{120 \text{ ounces}}{22 \text{ ounces/bottle}} \approx 5.45 \text{ bottles}
\][/tex]
Since we can only buy whole bottles, we need 6 bottles.
- A package of pretzels contains 16 ounces.
- Total pretzels needed are 30 ounces. To find the number of packages needed:
[tex]\[
\text{Packages needed} = \frac{30 \text{ ounces}}{16 \text{ ounces/package}} \approx 1.875 \text{ packages}
\][/tex]
Again, rounding up, we need 2 packages.

4. Calculate the total cost:
- Each bottle of sparkling water costs [tex]$1.50.
- Number of bottles needed = 6:
\[
\text{Total cost for sparkling water} = 6 \text{ bottles} \times \$[/tex]1.50 \text{ per bottle} = \[tex]$9.00
\]
- Each package of pretzels costs $[/tex]2.99.
- Number of packages needed = 2:
[tex]\[
\text{Total cost for pretzels} = 2 \text{ packages} \times \$2.99 \text{ per package} = \$5.98
\][/tex]

5. Calculate Kiran’s total budget:
[tex]\[
\text{Total budget} = \$9.00 + \$5.98 = \$14.98
\][/tex]

Going by the multiple-choice options provided:
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 choice is the one that refers directly to the cost calculation we performed:

Option D: [tex]\(1.50 \cdot 6 + 2.99 \cdot 2 = b\)[/tex]

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