/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 A "variety pack" of ramen noodle... [FREE SOLUTION] | 91Ó°ÊÓ

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A "variety pack" of ramen noodles consists of a dozen individual packs of noodles: six packs of chicken flavor, three packs of beef flavor, and three packs of vegetable flavor. (a) How many vegetable noodle packs are in the following numbers of variety packs: \(20,4.667,0.25 ?\) (b) How many variety packs are necessary to provide the following numbers of beef noodle packs: \(72,3,10 ?\) (c) How many vegetable noodle packs are there in the number of variety packs that contain each of the following numbers of the other flavors: 30 chicken flavor, 2 chicken flavor, 25 beef flavor? (For any inexact numbers, report your answers to four significant figures.)

Short Answer

Expert verified
(a) 60, 14.00, 0.75; (b) 24, 1, 4; (c) 15, 1.000, 25.00 vegetable packs.

Step by step solution

01

Understanding the 1 Pack Composition

A variety pack contains 12 packs in total: - 6 chicken flavor - 3 beef flavor - 3 vegetable flavor This information will help us solve part (a), (b), and (c) by identifying what portion of the packs are of each flavor.
02

Calculate Vegetable Packs for Part (a)

For each variety pack, there are 3 vegetable packs. - For 20 variety packs: total vegetable packs = 20 × 3 = 60 - For 4.667 variety packs: total vegetable packs = 4.667 × 3 = 14.001 packs - For 0.25 variety packs: total vegetable packs = 0.25 × 3 = 0.75 packs
03

Calculate Variety Packs Needed for Beef Packs in Part (b)

Each variety pack has 3 beef packs. To find how many variety packs are needed for a given number of beef packs: - For 72 beef packs: necessary variety packs = 72 ÷ 3 = 24 - For 3 beef packs: necessary variety packs = 3 ÷ 3 = 1 - For 10 beef packs: necessary variety packs = 10 ÷ 3 ≈ 3.333, which rounds up to 4 (since you can't have a fraction of a variety pack)
04

Calculate Vegetable Packs Based on Other Flavors for Part (c)

Use the given numbers of other flavors to find the number of variety packs, then use that to find the vegetable packs. - For 30 chicken packs (6 per variety pack): variety packs = 30 ÷ 6 = 5, then vegetable packs = 5 × 3 = 15 - For 2 chicken packs: variety packs = 2 ÷ 6 ≈ 0.3333, then vegetable packs = 0.3333 × 3 ≈ 1.000 (keep four significant figures) - For 25 beef packs (3 per variety pack): variety packs = 25 ÷ 3 ≈ 8.333, then vegetable packs = 8.333 × 3 ≈ 25.00 (keep four significant figures)

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Key Concepts

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

Flavor Distribution in Ramen Noodle Variety Packs
When dealing with ramen noodle variety packs, understanding the flavor distribution is key to solving related math problems. Each variety pack contains a total of 12 individual packs which include:
  • 6 packs of chicken flavor
  • 3 packs of beef flavor
  • 3 packs of vegetable flavor
This consistent distribution means that each variety pack always has the same number of each flavor. This allows you to predict how many packets of each flavor you'll get, based solely on the number of variety packs. Thus, multiplying the number of variety packs by the count for each flavor will give you the total for that flavor, providing a clear and simple approach to understanding the composition.
Arithmetic Calculations for Determining Quantity
Arithmetic is at the heart of solving any problem involving quantities, like those of ramen noodle packs. For example, if you need to find out how many vegetable packs are in a given number of full variety packs, you simply multiply the number of variety packs by the number of vegetable packs per variety. The formula looks like this:\[\text{Total Vegetable Packs} = \text{Number of Variety Packs} \times 3\]This kind of calculation lets you quickly ascertain the contents of any number of variety packs. Similarly, if you're tasked with finding how many variety packs you need for a certain number of beef packs, you'd use division:\[\text{Necessary Variety Packs} = \frac{\text{Total Beef Packs Needed}}{3}\]Understanding these basic arithmetic processes simplifies handling the requirements of each type of flavor.
Significant Figures in Rounding Solutions
Significant figures are crucial in presenting numbers that arise from calculations involving ramen noodle packs, particularly when exact division is not possible. For any calculation that doesn't result in a whole number, rounding is essential to match the appropriate level of precision. For instance, when computations yield numbers like 3.333, it's often necessary to round up because you can't practically have a fraction of a variety pack. Rounding to a whole number ensures the result is useful in a real-world context, such as when determining the number of necessary packs. Furthermore, keeping track of significant figures ensures you maintain precision in your results, which is particularly important when presenting answers in scientific or educational settings. It allows others to understand the accuracy and reliability of your numbers.
Pack Composition and Its Applications
Understanding the composition of a ramen noodle variety pack is instrumental in performing calculations and making practical decisions based on them. Each variety pack’s structure—with 6 chicken, 3 beef, and 3 vegetable packs—is consistent, providing a clear basis for formulating math problems and solutions. When faced with questions like determining the number of packs required for a certain amount of chicken or beef flavor, knowing the pack composition lets you set up equations quickly. This predictability allows you to apply the same calculations each time with confidence. For example, to find out how many vegetable packs are based on other flavor counts, you can determine the number of variety packs first from the other flavors, and then calculate the vegetable flavors using the fixed composition. This simplifies the process and removes guesswork, making problem-solving straightforward and efficient.

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Most popular questions from this chapter

A certain sample of coal contains 1.6 percent sulfur by mass. When the coal is burned, the sulfur is converted to sulfur dioxide. To prevent air pollution, this sulfur dioxide is treated with calcium oxide \((\mathrm{CaO})\) to form calcium sulfite \(\left(\mathrm{CaSO}_{3}\right) .\) Calculate the daily mass (in kilograms) of \(\mathrm{CaO}\) needed by a power plant that uses \(6.60 \times 10^{6} \mathrm{~kg}\) of coal per day.

Suppose you are given a cube made of magnesium (Mg) metal of edge length \(1.0 \mathrm{~cm} .\) (a) Calculate the number of \(\mathrm{Mg}\) atoms in the cube. (b) Atoms are spherical in shape. Therefore, the \(\mathrm{Mg}\) atoms in the cube cannot fill all the available space. If only 74 percent of the space inside the cube is taken up by \(\mathrm{Mg}\) atoms, calculate the radius in picometers of an \(\mathrm{Mg}\) atom. (The density of \(\mathrm{Mg}\) is \(1.74 \mathrm{~g} / \mathrm{cm}^{3},\) and the volume of a sphere of radius \(r\) is \(\left.\frac{4}{3} \pi r^{3} .\right)\)

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How much sulfur (in tons), present in the original materials. would result in that quantity of \(\mathrm{SO}_{2}\) ?

Aspirin or acetylsalicylic acid is synthesized by combining salicylic acid with acetic anhydride: $$ \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} $$ \(\begin{array}{l}\text { salicylic acid acetic anhydride } \\ \text { aspirin } & \text { acetic acid }\end{array}\) (a) How much salicylic acid is required to produce \(0.400 \mathrm{~g}\) of aspirin (about the content in a tablet), assuming acetic anhydride is present in excess? (b) Calculate the amount of salicylic acid needed if only 74.9 percent of salicylic is converted to aspirin. (c) In one experiment, \(9.26 \mathrm{~g}\) of salicylic acid reacts with \(8.54 \mathrm{~g}\) of acetic anhydride. Calculate the theoretical yield of aspirin an the percent yield if only \(10.9 \mathrm{~g}\) of aspirin is produced.

It is estimated that the day Mt. St. Helens erupted (May 18 , 1980 ), about \(4.0 \times 10^{5}\) tons of \(\mathrm{SO}_{2}\) were released into the atmosphere. If all the \(\mathrm{SO}_{2}\) were eventually converted to sulfuric acid, how many tons of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) were produced?

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