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Math  /  Algebra

Question(Algebra 1, Unit 2, Lesson 2) 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 $1.50\$ 1.50. A package of pretzels contains 16 ounces and costs $2.99\$ 2.99. Let nn represent number of people watching the football game, ss represent the ounces of sparkling water, pp represent the ounces of pretzels, and bb represent Kiran's budget in dollars. Which equation best represents Kiran's budget?
Select the correct choice. (A) 12s+3p=b12 s+3 p=b (B) 12⋅10+3⋅10=b12 \cdot 10+3 \cdot 10=b (C) 1.50s+2.99p=b1.50 s+2.99 p=b (D) 1.50⋅6+2.99⋅2=b1.50 \cdot 6+2.99 \cdot 2=b

Studdy Solution

STEP 1

1. Each person consumes 12 ounces of sparkling water and 3 ounces of pretzels.
2. There are 10 people, including Kiran's family.
3. A bottle of sparkling water contains 22 ounces and costs 1.50.<br/>4.Apackageofpretzelscontains16ouncesandcosts1.50.<br />4. A package of pretzels contains 16 ounces and costs 2.99.
5. We need to find an equation that represents Kiran's budget for the gathering.

STEP 2

1. Calculate the total ounces of sparkling water and pretzels needed.
2. Determine the number of bottles and packages needed.
3. Calculate the total cost and form the equation for Kiran's budget.

STEP 3

Calculate the total ounces of sparkling water needed for 10 people: s=12×10=120 ounces s = 12 \times 10 = 120 \text{ ounces}
Calculate the total ounces of pretzels needed for 10 people: p=3×10=30 ounces p = 3 \times 10 = 30 \text{ ounces}

STEP 4

Determine the number of bottles of sparkling water needed: Each bottle contains 22 ounces, so the number of bottles needed is: Bottles=12022≈5.45 \text{Bottles} = \frac{120}{22} \approx 5.45 Since we cannot buy a fraction of a bottle, we need 6 bottles.
Determine the number of packages of pretzels needed: Each package contains 16 ounces, so the number of packages needed is: Packages=3016≈1.875 \text{Packages} = \frac{30}{16} \approx 1.875 Since we cannot buy a fraction of a package, we need 2 packages.

STEP 5

Calculate the total cost: The cost for 6 bottles of sparkling water is: 6×1.50=9.00 dollars 6 \times 1.50 = 9.00 \text{ dollars}
The cost for 2 packages of pretzels is: 2×2.99=5.98 dollars 2 \times 2.99 = 5.98 \text{ dollars}
The total budget b b is: b=9.00+5.98=14.98 dollars b = 9.00 + 5.98 = 14.98 \text{ dollars}
The equation that represents Kiran's budget is: 1.50⋅6+2.99⋅2=b 1.50 \cdot 6 + 2.99 \cdot 2 = b
The correct choice is:
(D) 1.50⋅6+2.99⋅2=b \boxed{(D) \, 1.50 \cdot 6 + 2.99 \cdot 2 = b}

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