Lesson 4. Solving Word Problems Using Unit Rates. How much for just one? Problem Solving: Problem Solving: Solving Word Problems Using Unit Rates

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1 Problem Solving: Solving Word Problems Using Unit Rates Problem Solving: Solving Word Problems Using Unit Rates How much for just one? Often we may want to know the value of just one of something. The value of one of something is called the unit rate. We use this concept often without actually thinking about unit rate. For instance, in the grocery store, it is easier if we compare the cost of just one unit, such as an ounce or a pound. If we see a sign advertising four boxes of cereal for $0, we might ask ourselves how much it costs for just one box. Let s look at a problem involving unit rate. Example It costs $6 to buy cartons of milk. What is the cost of carton? Set up a proportion with a variable. Carton $6 = x x is the cost for carton. Complete the proportion by finding the value of x. Carton $6 = $2 One carton of milk costs $2. The unit rate is $2 per carton. Unit Lesson 2

2 Another way we talk about unit rate is when we use the term miles per hour. This term means the number of miles we travel in one hour. Miles per hour is a unit rate. It s the value of just one of something every one hour. Example 2 shows this situation. Example 2 Quentin s dad drove him to a soccer tournament. They drove 20 miles in hours. About how far did they drive in just hour? What was the rate in miles per hour? Set up a proportion with a variable. Miles Hour 20 = m m is the miles traveled in hour. Complete the proportion by finding a value for m. Miles Hour 20 = 60 We see now that m = 60. This means Quentin and his dad drove 60 miles in hour. Another way of saying this is 60 miles per hour. The unit rate is 60 miles per hour. Notice that each proportion starts with the units written in words. Writing the words out is a good habit to practice with this type of problem. We want to remind ourselves what the numbers stand for. That way, when we solve for a variable, we know exactly what that variable represents. In the example about Quentin and his dad, the variable m stands for miles. In the previous example, the variable x stands for the cost in dollars. Example shows another problem involving unit rate. 26 Unit Lesson

3 Example We are at the state fair. We use tickets to pay for the rides. Each ride requires the same number of tickets. We can take rides on 20 tickets. How many tickets does it take for ride? Set up a proportion with a variable. Tickets Ride 20 = t t stands for the number of tickets. Complete the proportion by finding the value for t. Tickets Ride 20 = We can see that t =. We need tickets to take ride. Unit Lesson 27

4 How do we solve word problems using unit rates? Sometimes we have to compute the unit rate for something to find the better deal. We usually expect that items marked for $ or for $ are better deals than buying just one item. However, this is not always the case. To compare these different pricing methods, we find the unit rate. Example shows how we analyze this type of situation to determine the better deal. Example Monica needs soup. The store has a special cans for $0. If she buys just can of soup, the cost is $2.20. Which is the better deal? We compare the cost of can of soup for $2.20 to the special deal of cans for $0. We set up a proportion to find the unit rate. Number of Cans $0 = x First we ask ourselves,? =? The answer is. Then we need to find the value for x in the statement, x = $0. It s $2. We complete the proportion by filling in the value for x. Number of Cans $0 = $2 The unit price is $2. We now compare the unit rate of $2 to the cost for can $2.20. Buying soup at for $0 is the better deal because it s $2 per can, not $2.20 per can. Grocery stores often use this pricing method. We expect items marked for $ to be the best deals. However, that is not always the case. 28 Unit Lesson

5 Example 2 shows a different situation. Sometimes the special pricing methods are not the best deal. Example 2 Marcus needs to wear ties for his new job. At the department store, ties are $9 each or for $60. We need to compare the cost of just tie to the special deal by finding the unit rate. We set up the proportion like this: Number of Ties $60 = x First we ask ourselves,? =? The answer is. Then we need to find the value for x in this statement, x = $60. The cost is $20. We complete the proportion by filling in the value for x. Number of Ties $60 = $20 When we compare the two pricing methods, we see that the special deal is not the better deal. The unit rate is $20 per tie. If we buy the ties individually, they are $9 per tie. Problem-Solving Activity Turn to Interactive Text, page 08. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. Unit Lesson 29

6 Homework Activity Simplify the ratios. Model Activity Answer: 6 2 = Set up the unit rate problems as proportions. Tell what the variable represents. Show the units in words. Model It costs $8 for sandwiches. How much does it cost for just sandwich? Answer: $8 Sandwich = x $8 Sandwich = $2 X stands for the cost of sandwich. The cost of one sandwich is $2.. Nguyen paid $0 for CDs. If all cost the same amount, what was the cost of just CD? $0 $0 CD 2. Sheldon paid $80 for 6 pairs of contact lenses. What was the cost of just pair of lenses? $80 $0 Pair 6. Britt can do sit-ups in minutes. How many sit-ups can she do in just minute? Sit ups Minutes Activity Tell the better deal in each case by finding the unit rate.. What s the better deal, apple for $.0, or for $? 2. What s the better deal, pair of jeans for $60 or for $200?. What s the better deal, T-shirt for $9 or 2 for $0?. What s the better deal, CD for $ or 2 for $2?. What s the better deal, juices for $ or $.7 for juice in the vending machine? 260 Unit Lesson Copyright 200 by Cambium Learning Sopris West. All rights reserved. Permission is granted to reproduce this page for student use.

7 Homework Activity Distributed Practice Solve = x 2. w = = z. a + 8 = = b = c = d 8. e 7 = 0 Copyright 200 by Cambium Learning Sopris West. All rights reserved. Permission is granted to reproduce this page for student use. Unit Lesson 26