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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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Most popular questions from this chapter

Scientific theory holds that convergent evolution occurs when different species independently evolve analogous structures, or features that may appear different, but perform the same function. Creatures evolve such structures in order to adapt to their environments. A scientist argues that bats and birds have analogous structures. Which of the following supports his argument? A. Bats use echolocation to track their prey, while birds rely primarily on sight. B. Unlike bird wings, bat wings are composed primarily of membrane, but both types of wings provide flight capabilities. C. Baby bats gain nourishment from their mother's milk, while baby birds eat worms and bugs brought by their mothers. D. Both bats and birds frequently make their homes in trees, bridges, and attics.

Which idea about city government is included in the Affirmative? A. City governments require a separate council to legislate business and administrative concerns. B. The deplorable conditions of the cities are caused by economic and social factors. C. Checks and balances between departments are the only way to guarantee successful government. D. Many cities have completely revised the structure of their municipal governments.

A shaved ice stand located near a beach records its hourly revenue as well as the temperature outside, as shown on the graph above. Approximately how much more revenue would be expected during a 3-hour shift with a temperature of \(100^{\circ}\) than at a shift of the same duration with a temperature of \(90^{\circ}\) ? A. $$\$ 150$$ B. $$\$ 500$$ C. $$\$ 750$$ D. $$\$ 1,500$$

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Which of the following would most likely result in an increase in the use of nuclear power? A. the invention of a safe radioactive-waste disposal method B. the discovery of a cleaner method of burning coal C. a decrease in taxes on fossil fuels D. increased oil exploration in Alaska
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