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Chapter 2: Problem 22

A jar of marbles contains two sizes of marbles: normal and jumbo. There are 84 normal size marbles. If \(\frac{2}{9}\) of the marbles are jumbo size, then how many marbles total are in the jar? A. 19 B. 103 C. 108 D. 378

Short Answer

Expert verified
The total number of marbles in the jar is 108. The correct option is C. 108.

Step by step solution

01

Find the number of jumbo marbles

Let x be the total number of marbles in the jar. According to the problem, \(\frac{2}{9}\) of the marbles are jumbo size. So, the number of jumbo marbles can be written as \(\frac{2x}{9}\). We know there are \(84\) normal marbles, so we can write the equation as: \[\frac{7}{9}x = 84\]
02

Solve the equation to find the total number of marbles

Now we need to solve the equation for x, which will give us the total number of marbles in the jar. \[\frac{7}{9}x = 84\] To solve for x, multiply both sides by \(\frac{9}{7}\): \[x = \frac{9}{7} \cdot 84\] \[x = 9 \cdot 12\] \[x = 108\] So, there are 108 marbles in total in the jar.
03

Choose the correct option

Now that we have found the total number of marbles, we can compare our answer to the given options: A. 19 B. 103 C. 108 D. 378 Since 108 is among the choices, the correct answer is: C. 108

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Key Concepts

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

Ratio and Proportion
Understanding ratio and proportion is essential when facing problems that involve comparing quantities or scaling numbers in proportion to one another. A ratio simply compares two quantities, often in the form 'A to B' or as a fraction like \( \frac{A}{B} \). When we talk about proportion, we are dealing with an equation that shows two ratios are equivalent.

For example, if we have a scale model where 1 inch represents 5 miles, we have a ratio of 1 to 5. If our model is 2 inches long, then the actual distance represented is in proportion to the scale, which in this case would be 10 miles. This ratio (scale model to actual size) remains constant.

In our exercise, we use proportion to determine the total number of marbles in a jar. We know that the ratio of jumbo to normal size marbles is \( \frac{2}{9} \). Using this, we can set up a proportional relationship (\

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The passage below is incomplete. For each 鈥淪elect鈥� option, choose the option that correctly completes the sentence. (For this practice test, circle your selection.) To: All Personnel Billie Tanker Pipe and Supply From: Billie Tanker Date: March 18, 2013 Subject: Farewell to Ron Jensen Here at Billie Tanker Pipe and Supply, we take pride in our unparalleled customer service and the unquestionable quality of our work. Though we have expanded our operations from one small storefront to a county-wide franchise, we continue to see all our workers, from truck drivers to senior management, as members of one large family. Therefore, it is with a mixed sense of pride and sadness that I congratulate Ron Jensen on his retirement. Ron started at our company fifteen years ago and was a part of growth from making small business 鈥渉ousecalls鈥� to servicing major corporations in our city. Many customers got to know Ron by name and asked for him personally when they needed an estimate. Ron鈥檚 service record is outstanding. His work one-on-one with clients and the knowledge he鈥檚 gained from a decade and a half in the field many referrals from valued customers. While many of his peers went on to positions in management, Ron remained at the 鈥渇ront lines,鈥� where he could 鈥済et his hands dirty鈥� with the renovations and retrofits that he preferred to desk work. At his retirement to his colleague of many years, Belle Sanchez. His coworkers will then stage a humorous 鈥淭his Was Your Life鈥� retrospective, highlighting Ron鈥檚 career successes, and relating humorous anecdotes about his adventures in engineering. Ron plans to retain a consultant relationship with our company to best serve his long-time clients, providing guidance necessary to make his transition to retirement as smooth as possible for all parties. Ron will work with new technicians as they take over existing projects, to ensure our best performance. Please join me in thanking Ron for his outstanding tenure of service and commending him on a successful career. All employees are invited to Ron鈥檚 retirement party on Friday, at 7pm, in the main conference room of our downtown office location: 2121 Main Street. Come wish him a happy retirement.
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