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Chapter 11: Problem 9

Vicki is selling bags of caramel corn at her booth at the state fair at a rate of 5 bags per hour. By noon, she had sold 15 bags. She will have sold a total of 40 bags at \begin{tabular}{|l|l|} \hline Select... & \(\nabla\) \\ \hline \(4: 00 \mathrm{PM}\) & \\ \hline \(5: 00 \mathrm{PM}\) \\ \hline 6:00 PM \\ \hline \end{tabular}

Short Answer

Expert verified
5:00 PM.

Step by step solution

01

- Identify Initial Conditions

By noon, Vicki had sold 15 bags of caramel corn.
02

- Determine Amount Remaining to be Sold

Vicki needs to sell a total of 40 bags. Since she has already sold 15 bags, the remaining number of bags to be sold is calculated by:\[ 40 - 15 = 25 \]
03

- Calculate the Time Needed to Sell Remaining Bags

Vicki sells bags at a rate of 5 bags per hour. To find the time needed to sell the remaining 25 bags, we use the formula:\[ \text{Time} = \frac{\text{number of bags}}{\text{rate}} = \frac{25}{5} = 5 \text{ hours} \]
04

- Determine the Time Vicki Will Reach 40 Bags

Since Vicki needs an additional 5 hours from noon (12:00 PM) to sell the remaining bags, we add 5 hours to 12:00 PM:\[ 12:00 \text{ PM} + 5 \text{ hours} = 5:00 \text{ PM} \]
05

- Select the Correct Option

By following the above steps, it is determined that Vicki will have sold a total of 40 bags by 5:00 PM.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

rate calculation
Understanding the concept of rate is crucial for solving time-rate-distance problems. Rate typically refers to the number of units per a specific measure of time. In this exercise, Vicki's rate of selling caramel corn is 5 bags per hour. When calculating how long it takes to achieve a specific total, you can divide the remaining quantity by the rate. For instance, to find out how long it will take Vicki to sell 25 more bags at 5 bags per hour, we use \( \text{Time} = \frac{\text{remaining bags}}{\text{rate}} \). This calculation yields 5 hours. Knowing the rate can simplify otherwise complex problems.
GED math
Time-rate-distance problems like this one frequently appear on GED math tests. These problems assess your ability to apply basic algebra and arithmetic to real-world scenarios. To master GED math, it is essential to understand the relationships between variables such as time, rate, and distance (or in this case, the number of bags sold). Here, you should focus on identifying initial conditions, calculating remaining quantities, and finding the right formula to apply. Practicing these steps regularly will improve your confidence and performance in GED math sections.
time management
Effective time management is key to solving multi-step problems efficiently. Begin by identifying known quantities and determine what you need to find. In the current exercise, start with the given number of bags sold by noon (15 bags). Next, define the total number of bags to be sold (40 bags). Calculate the remaining quantity (25 bags), and then determine time by considering the rate. This organized approach helps manage your time better during exams, ensuring you complete problems more quickly and accurately. Breaking a problem into smaller, manageable steps is a valuable exam technique.
problem-solving skills
Building strong problem-solving skills involves understanding the problem, planning your approach, solving step by step, and reviewing your solution. In this exercise, the steps were: identify initial conditions, calculate the remaining amount to be sold, determine the time needed based on the rate, and then calculate the final time. Apply these steps to various problems to strengthen your skills. Additionally, always double-check your work. Confirm whether your final answer makes sense in the context of the problem. This practice will make you more adept at tackling a wide range of math problems.

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Most popular questions from this chapter

Constance is controlling the flow of a solution into a graduated cylinder. She wants to go to lunch and decides to set the flow at a lower rate rather than shut it off completely. The cylinder already holds 72 milliliters of solution and can hold a maximum of 500 milliliters. If \(r\) represents the rate at which the flow is set in milliliters per minute, which inequality could Constance solve to determine a safe range of flow rates, assuming she plans to take 60 minutes for lunch? A. \(72 r+60 \geq 500\) B. \(72 r+60 \leq 500\) C. \(60 r+72 \geq 500\) D. \(60 r+72 \leq 500\)

Aaron is earning money by mowing lawns. He charges \(\$ 40\) per lawn. He is trying to save up at least \(\$ 1500\) for a new riding lawnmower. \(\mathrm{He}\) already has \(\$ 420\). Which inequality best represents Aaron's riding lawnmower goal? A. \(420 x+40 \geq 1500\) B. \(40 x+420 \geq 1500\) C. \(420 x+40 \leq 1500\) D. \(40 x+420 \leq 1500\)

A rock dropped from a 1024-foot-high cliff falls a distance \(D\) given by \(D=16 t^2\), where \(t\) is the time in seconds after the rock is dropped. How long will it take the rock to reach the bottom of the cliff? A. 64 seconds B. 32 seconds C. 16 seconds D. 8 seconds

As a goodwill gesture, Florence is giving \(\$ 5\) to each person who participates in a public cleanup program. She started with \(\$ 400\). After two hours, she had already given away \(\$ 135\). Which inequality represents the number of people she can still give \(\$ 5\) to? A. \(p \leq 51\) B. \(p \leq 52\) C. \(p \leq 53\) D. \(p \leq 54\)

The length of a rectangle is 5 centimeters more than the width. The perimeter of the rectangle is 90 centimeters. What is the length of the rectangle? A. 15 centimeters B. 18 centimeters C. 22.5 centimeters D. 25 centimeters
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