Petr has $95 to shop for clothes. He goes to his favorite store and sees that most of the clothing items are on sale. He places two shirts, one pair of pants and a light jacket in his shopping cart. The prices of the items are: $12.99, $15.79, $24.75 and $33.15. Petr decides to estimate the total cost to make sure that he has enough money to pay for all of the items in the cart. Can you estimate how much the items in his cart will cost?

In this concept, you will learn when estimation is a reasonable option to solve problems.

### Using Estimation to Solve Problems

You can use estimation in several different situations. To use estimation, you need to read and understand the problem. There will be clues in the problem to let you know if estimation is a good option for solving that specific problem.

**Estimating** means finding an answer that is an approximate answer. When estimating, your answer must make sense, but it does not need to be exact. You need to find an answer that is reasonable.

When looking at a problem, read the problem to see if estimation is a good option. You can look for key words to help us with this. Here are some of the key words that suggest estimation:

- Close to
- Approximate
- Estimate
- An answer that makes sense
- About

If you see these words in a word problem, you can estimate to find the answer.

Let's look at an example.

Marcus wants to get an idea how much he is spending at the grocery store. On the way to the checkout, he looks at the items in his cart. Here are the prices of the food in his cart: $0.50, $2.50, $3.45 and $6.79. About how much will Marcus spend when he checks out?

Are there any key words in this problem?

Yes, the word "about" lets you know that you can estimate to find the answer.

Next, use rounding and round to the nearest whole number.

0.50 becomes 1

2.50 becomes 3.00

3.45 becomes 3.00

6.79 becomes 7

Then, add up the rounded answers: 1 + 3 + 3 + 7 = 14.

The answer is $14.00. Marcus will spend approximately $14.00 at the store.

### Examples

#### Example 1

Earlier, you were given a problem about Petr and his shopping cart.

Petr has $95 to pay for the items. He has items in his cart that cost $12.99, $15.79, $24.75 and $33.15. What is the estimated cost of the items in Petr's cart?

First, round each value to the nearest dollar.

12.99 becomes 13

15.79 becomes 16

24.75 becomes 25

33.15 becomes 33

Next, add the rounded values.

13 + 16 + 25 + 33 = 87

Then, write the estimated cost.

87

The answer is $87. Petr's items will cost approximately $87, so he has enough money to buy the items.

#### Example 2

Tyrone is working to buy presents for his family for the holidays. He has picked out a CD for his sister for $14.69, a vase for his mother at $32.25 and a picture frame for his father at $23.12. What is the estimated total cost of Tyrone's purchases?

First, round each price to the nearest dollar.

32.25 rounds to 32

23.12 rounds to 23

Next, add the rounded values.

32 + 23 = 55

Then, write the estimated cost.

55

The answer is $55. Tyrone will spend approximately $55.

#### Example 3

Kelly bought a shirt for $26.78 and a pair of pants for $25.10. What is the estimated total cost of her purchases?

First, round each value to the nearest dollar.

26.78 becomes 27

25.10 becomes 25

Next, add the rounded values.

27 + 25 = 52

Then, write the estimated cost.

52

The answer is $52. Kelly will spend approximately $52.

**Example 4**

Julia ran 16.5 miles one day and 22.8 miles the next. What is her estimated total mileage?

First, round each distance to the nearest mile.

16.5 becomes 17

22.8 becomes 23

Next, add the rounded values.

17 + 23 = 40

Then, write the estimated mileage.

40

The answer is 40 miles. Julia ran approximately 40 miles.

**Example 5**

Keisha biked 25.75 miles one day and 16.2 miles the next. What is her estimated total mileage?

First, round each distance to the nearest mile.

25.75 becomes 26

16.2 becomes 16

Next, add the rounded values.

26 + 16 = 42

Then, write the estimated mileage.

42

The answer is 42 miles. Keisha biked approximately 42 miles.

### Review

Look at each problem and use what you have learned about estimation to solve each problem.

- Susan is shopping. She has purchased two hats at $5.95 each and two sets of gloves at $2.25 each. If she rounds each purchase price, how much can she estimate spending?
- If she uses front–end estimation, how does this change her answer?
- Which method of estimation gives us a more precise estimate of Susan’s spending?
- If she brings $20.00 with her to the store, about how much change can she expect to receive?
- If she decided to purchase one more pair of gloves, would she have enough money to make this purchase?
- Would she receive any change back? If yes, about how much?
- Mario is working at a fruit stand for the summer. If a customer buys 3 oranges at $.99 a piece and two apples for $.75 a piece, about how much money will the customer spend at the fruit stand? Use rounding to find your answer.
- What is the estimate if you use front–end estimation?
- Why do you think you get the same answer with both methods?
- If the customer gives Mario a $10.00 bill, about how much change should the customer receive back?
- Christina is keeping track of the number of students that have graduated from her middle school over the past five years. Here are her results.

2004 – 334

2005 – 367

2006 – 429

2007 – 430

2008 – 450

Estimate the number of students who graduated in the past five years.

- Did you use rounding or front–end estimation?
- Why couldn’t you use front–end estimation for this problem?
- Carlos has been collecting change for the past few weeks. He has 5 nickels, 10 dimes, 6 quarters and four dollar bills. Write out each money amount.
- Use rounding to estimate the sum of Carlos’ money.
- Use front–end estimation to estimate the sum of Carlos’ money.
- Which method gives you a more accurate estimate? Why?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.24.