5.14: Fundamentals 13 - Rates
- Page ID
- 148801
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By the end of this lesson, you should understand
- a rate is a special ratio that compares two quantities of different units
- a unit rate is a ratio where the denominator is a unit of one.
- units can add meaning to specific situations.
By the end of this lesson, you should be able to
- write a rate as a fraction.
- simplify a rate by a unit factor.
- use unit rates to compare values.
FUNDAMENTALS OF THE LESSON
A ratio is a comparison of two quantities. If a bowl has 12 pieces of fruit in it and 5 of those are apples, the ratio of apples to the fruit in the bowl is 5 to 12. This ratio could also be written as 5:12 or as a fraction, 5/12.
A rate is a special ratio that compares two quantities of different units. If you buy 10 apples for $3.00, we say the cost is $3.00 per 10 apples. Rates are often used in our everyday lives. How much money you make per hour, how many miles per hour you are driving, and how much you pay for food per pound are examples of rates. Rates can be used to determine costs, like gas prices (dollars per gallon), or be used to express certain measurements in healthcare, like pulse rates (beats per minute).
A unit rate means that we have a rate of one of some quantity. For example, what is the price of one apple, if you paid $3.00 for 10 apples? You are paying 30 cents for 1 apple. Both $3.00 for 10 apples and $0.30 for 1 apple are rates, but $0.30 for 1 apple is a unit rate.
What is the rate?
Rob has a mowing service and charges $280 to mow eight different spaces in a local petting zoo. It usually takes Rob 7 hours to mow the lawn spaces before he is finished working for the day. The petting zoo has 62 different species and over 300 animals in it.
1. What is Rob’s price for mowing each lawn space? Hint: Assume the rate he charges for each lawn space at the petting zoo is the same.
2. What is Rob’s hourly wage?
3. A. How much should Rob charge if he mows 5 lawn spaces?
B. How much will Rob make an hour if it takes Rob 2.5 hours to mow these 5 spaces?
NEXT STEPS
Do you have enough?
You travel to the local Farmers Market for fresh produce. You have $20 left in your grocery budget for the month and want to buy the items in the left column in the table below. The right column shows the price for each item.
4. Do you have enough money to purchase the following list of items at the Farmers Market? Hint: You can use the quantity of an item and the cost of an item ($ / item) to find the price of the item.
|
Produce List |
Farmers Market Pricing |
|
6 sweet potatoes 8 ears of corn 8 apples 2.5 lbs. bananas 0.5 lbs. broccoli 1 lb. mushrooms 3 zucchini 1.5 lbs. carrot 2 lbs. onions |
Apples: 5 for $1.00 Bananas: $0.68/lb. Broccoli: $1.30/lb. Carrots: $2.50/lb. Corn: 5 for $2.00 Mushrooms: $0.45 per ¼ lb. Onions: $3.00/5 lbs. Sweet Potatoes: $0.70 each Zucchini: 12 for $3.00 |
A. Cost of sweet potatoes =
B. Cost of corn =
C. Cost of apples =
D. Cost of bananas =
E. Cost of broccoli =
F. Cost of mushrooms =
G. Cost of Zucchini =
H. Cost of carrots =
I. Cost of onions =
J. Total =
FURTHER APPLICATIONS
5. The 2019 VW Jetta has a highway rating of 41 miles per gallon. You plan to make a summer road trip from Morrisville, New York to Myrtle Beach, South Carolina. The distance is about 788 miles one way.
A. If the primary route to Myrtle Beach is I-95 south (highway driving), how many gallons of fuel will you need for the whole trip, there and back? Round to one decimal place.
B. If fuel costs an average of $2.35 a gallon, use your rounded answer from part A to determine the fuel cost for the whole trip.
6. Catrina needs to ride her bike to her friend’s house 96 miles away. She is riding at an average rate of 15 miles per hour. She has 6 hours to get there. Will she make it? Explain.
Questions: Rates
1. A Honda Civic car dealer has 6 black cars, 8 white cars, and 14 silver cars. What is the ratio of black cars to silver cars? Simplify the ratio.
2. Four pounds of meat cost $5. Choose the best choice that represents the rate given.
i. \(\dfrac{1\;lb}{4\;lb}\;and\;\dfrac{5 \;lb}{\$4}\)
ii. \(\dfrac{4\;lb}{\$5}\;and\;\dfrac{\$5}{4\;lb}\)
iii. \(\dfrac{\$4}{5\;lb}\;and\;\dfrac{5\;lb}{\$4}\)
3. 3 kiwis cost $1.80.
A. What is the cost per kiwi?
B. At this rate, what is the cost of 13 kiwis?
4. If David earns $100 in 8 hours, how much will he earn in 3 hours at the same rate? Round to the nearest cent, when appropriate.
5. If a car is traveling at a rate of 50 miles per hour, how far will it travel in 4 hours?
6. A plane flies 750 miles in 5 hours. How fast did the plane fly in one hour?
7. A box of crackers contains 7 servings and has a total of 420 calories.
A. How many calories are in 1 serving?
B. How many calories are in 4 servings?
8. A store sells bundles of shirts in three ways: 6 shirts for $25.50, 4 shirts for $18.00 or 5 shirts for $21.00.
A. Which is the better buy?
B. What is the unit rate of the best buy?
9. Sarah can make 38 dozen cupcakes in 8 days. How many dozen cupcakes can Sarah make in 5 days? Round to the nearest dozen cupcakes.
10. A pizza place sells pepperoni pizzas to cheese pizzas in a ratio of 9:4. If 14 cheese pizzas are sold in one day, how many pepperoni pizzas were sold on that day? Round to the nearest whole pizza.