Answer :
To find the equation that best represents Kiran's budget, let's go through the details step-by-step.
1. Calculate the total ounces of sparkling water and pretzels needed:
- Each person will be served 12 ounces of sparkling water and 3 ounces of pretzels.
- There are 10 people in total (including Kiran's family).
Total ounces of sparkling water [tex]\(s\)[/tex]:
[tex]\[
s = 12 \text{ ounces/person} \times 10 \text{ people} = 120 \text{ ounces}
\][/tex]
Total ounces of pretzels [tex]\(p\)[/tex]:
[tex]\[
p = 3 \text{ ounces/person} \times 10 \text{ people} = 30 \text{ ounces}
\][/tex]
2. Calculate the number of bottles of sparkling water and packages of pretzels needed:
- Each bottle of sparkling water contains 22 ounces and costs [tex]$1.50.
- Each package of pretzels contains 16 ounces and costs $[/tex]2.99.
Number of bottles of sparkling water needed:
[tex]\[
\text{Bottles needed} = \left\lceil \frac{120 \text{ ounces}}{22 \text{ ounces/bottle}} \right\rceil = 6 \text{ bottles}
\][/tex]
Number of pretzel packages needed:
[tex]\[
\text{Packages needed} = \left\lceil \frac{30 \text{ ounces}}{16 \text{ ounces/package}} \right\rceil = 2 \text{ packages}
\][/tex]
3. Calculate the total cost:
- Cost of sparkling water:
[tex]\[
\text{Cost of water} = 6 \text{ bottles} \times \$1.50/\text{bottle} = \$9.00
\][/tex]
- Cost of pretzels:
[tex]\[
\text{Cost of pretzels} = 2 \text{ packages} \times \$2.99/\text{package} = \$5.98
\][/tex]
- Total cost [tex]\( b \)[/tex]:
[tex]\[
b = \$9.00 + \$5.98 = \$14.98
\][/tex]
After these calculations, the numerical result is a total budget (cost) of \$14.98.
Let's match each option to this budget.
- Option (a): [tex]\( 12 s + 3 p = b \)[/tex]
- Option (b): [tex]\( 12 \cdot 10 + 3 \cdot 10 = b \)[/tex]
- Option (c): [tex]\( 1.50 s + 2.99 p = b \)[/tex]
- Option (d): [tex]\( 1.50 \cdot 6 + 2.99 \cdot 2 = b \)[/tex]
The correct representation is found in Option (d):
[tex]\[
1.50 \cdot 6 + 2.99 \cdot 2 = 14.98
\][/tex]
Based on this, the equation that best represents Kiran’s budget is:
[tex]\[
\boxed{1.50 \cdot 6 + 2.99 \cdot 2 = b}
\][/tex]
1. Calculate the total ounces of sparkling water and pretzels needed:
- Each person will be served 12 ounces of sparkling water and 3 ounces of pretzels.
- There are 10 people in total (including Kiran's family).
Total ounces of sparkling water [tex]\(s\)[/tex]:
[tex]\[
s = 12 \text{ ounces/person} \times 10 \text{ people} = 120 \text{ ounces}
\][/tex]
Total ounces of pretzels [tex]\(p\)[/tex]:
[tex]\[
p = 3 \text{ ounces/person} \times 10 \text{ people} = 30 \text{ ounces}
\][/tex]
2. Calculate the number of bottles of sparkling water and packages of pretzels needed:
- Each bottle of sparkling water contains 22 ounces and costs [tex]$1.50.
- Each package of pretzels contains 16 ounces and costs $[/tex]2.99.
Number of bottles of sparkling water needed:
[tex]\[
\text{Bottles needed} = \left\lceil \frac{120 \text{ ounces}}{22 \text{ ounces/bottle}} \right\rceil = 6 \text{ bottles}
\][/tex]
Number of pretzel packages needed:
[tex]\[
\text{Packages needed} = \left\lceil \frac{30 \text{ ounces}}{16 \text{ ounces/package}} \right\rceil = 2 \text{ packages}
\][/tex]
3. Calculate the total cost:
- Cost of sparkling water:
[tex]\[
\text{Cost of water} = 6 \text{ bottles} \times \$1.50/\text{bottle} = \$9.00
\][/tex]
- Cost of pretzels:
[tex]\[
\text{Cost of pretzels} = 2 \text{ packages} \times \$2.99/\text{package} = \$5.98
\][/tex]
- Total cost [tex]\( b \)[/tex]:
[tex]\[
b = \$9.00 + \$5.98 = \$14.98
\][/tex]
After these calculations, the numerical result is a total budget (cost) of \$14.98.
Let's match each option to this budget.
- Option (a): [tex]\( 12 s + 3 p = b \)[/tex]
- Option (b): [tex]\( 12 \cdot 10 + 3 \cdot 10 = b \)[/tex]
- Option (c): [tex]\( 1.50 s + 2.99 p = b \)[/tex]
- Option (d): [tex]\( 1.50 \cdot 6 + 2.99 \cdot 2 = b \)[/tex]
The correct representation is found in Option (d):
[tex]\[
1.50 \cdot 6 + 2.99 \cdot 2 = 14.98
\][/tex]
Based on this, the equation that best represents Kiran’s budget is:
[tex]\[
\boxed{1.50 \cdot 6 + 2.99 \cdot 2 = b}
\][/tex]
