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Chapter 6: Problem 1

Define the key terms. a. Rate b. Unit rate c. Unit cost

Short Answer

Expert verified
Rate is a ratio of two quantities; unit rate is a rate with a denominator of one; unit cost is cost per unit.

Step by step solution

01

Define Rate

A rate is a ratio between two related quantities. It expresses how one quantity changes in relation to another. For example, speed is a rate expressing distance over time, such as miles per hour.
02

Define Unit Rate

A unit rate is a rate in which the second quantity in the comparison is one unit. It simplifies a rate to per single unit of the denominator, such as 60 miles per hour or 5 dollars per pound.
03

Define Unit Cost

A unit cost is a type of unit rate where the total cost is divided by the number of units produced or consumed. This shows the cost per one unit of the good or service, such as 2 dollars per item.

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Key Concepts

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

Rate
When we talk about a rate, we're discussing a special kind of ratio. A rate compares two different types of quantities.
For instance, take speed. Speed measures how much distance (like miles) you can travel over a set amount of time (like hours or minutes).
If you say your car is traveling at 60 miles per hour, that means for every hour you drive, you cover 60 miles.
Rates can apply to many different situations:
  • Heartbeats per minute (bpm)
  • Steps taken per second
  • Calories burned per workout
Remember, what makes a rate special is how it reveals the relationship between two different quantities.
Unit Rate
A unit rate takes the idea of a rate and simplifies it even further.
It describes how much of one quantity corresponds to just a single unit of another quantity.
For example, if you say a car travels at 60 miles per hour, you鈥檙e describing a unit rate. That鈥檚 because you鈥檙e stating the distance you travel (60 miles) in exactly one hour.
Simplifying rates to unit rates can make them easier to understand and compare:
  • If 10 apples cost 5 dollars, the unit rate (cost per apple) would be 5 dollars/10 apples = 0.5 dollars per apple.
  • If a printer prints 300 pages in 5 minutes, the unit rate (pages per minute) would be 300 pages/5 minutes = 60 pages per minute.
By converting rates to unit rates, you can more easily compare different situations and make informed decisions.
Unit Cost
The concept of unit cost is very similar to unit rate, but it specifically focuses on cost.
Unit cost tells you the price for each single unit of a product or service.
For example, if a pack of 5 pens costs \(10, the unit cost is the total cost divided by the number of units:
  • \text{Unit cost} = \frac{\text{Total cost}}{\text{Number of units}} = \frac{10}{5} = 2 \text{ dollars per pen}
Knowing the unit cost is particularly helpful when comparing prices.
Say you鈥檙e in a store and you see that a 12-pack of soda costs \)6, while a 24-pack costs $11. You can find the unit cost for each option and decide which is the better deal:
  • 12-pack unit cost: \frac{6}{12} = 0.50 \text{ dollars per can}
  • 24-pack unit cost: \frac{11}{24} \text{ (approximately)} = 0.46 \text{ dollars per can}
In this case, the 24-pack offers a lower unit cost per can, making it the better buy.

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Most popular questions from this chapter

Laws have been instituted in Florida to help save the manatee. To establish the number in Florida, a sample of 150 manatees was marked and let free. A new sample was taken and found that there were 3 marked manatees out of 40 captured. What is the approximate population of manatees in Florida?

A cheetah can run \(120 \mathrm{m}\) in 4.1 sec. An antelope can run \(50 \mathrm{m}\) in 2.1 sec. Compare their unit speeds to determine which animal is faster. Round to the nearest whole unit.

Write the ratio in lowest terms with whole numbers in the numerator and denominator. \(\$ 16.80\) to \(\$ 2.40\)

Carbonated beverages come in different sizes and contain different amounts of sugar. Compute the amount of sugar per fluid ounce for each soda. Then determine which has the greatest amount of sugar per fluid ounce. $$\begin{array}{l|c|c} \text { Soda } & \text { Amount } & \text { Sugar } \\ \hline \text { Coca-Cola } & 20 \mathrm{fl} \mathrm{oz} & 65 \mathrm{g} \\ \hline \text { Mello Yello } & 12 \mathrm{fl} \mathrm{oz} & 47 \mathrm{g} \\ \hline \text { Canada Dry } & 8 \mathrm{fl} \mathrm{oz} & 24 \mathrm{g} \\ \text { Ginger Ale } & & \\ \hline \end{array}$$

Write the ratio in two other ways. $$\frac{1}{2}$$
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