Draw a Picture

The three towns of Garden City, Scott City, and Oakley are located along a straight highway. The distance between Garden City and Oakley is 81 mi. Scott City is located between Garden City and Oakley and is 36 mi. from Garden City. How far is it from Scott City to Oakley?

Example 1

Think: What is the relationship of these towns to each other? Use a picture to show the relationship.Garden City

Scott City

Oakley

36 81

Think: What is being asked? What mathematical operator does the relationship suggest?Represent the unknown with a variable: d = the distance from Scott City to Oakley.Use the picture to select the operation of addition: d + 36 = 81.

Think: How is the equation solved?Subtract 36 from both sides of the equation: d + 36 – 36 = 81 – 36.The distance from Scott City to Oakley is 45 mi.

Think: As you look back at the diagram, does 45 mi. seem reasonable considering the facts given in the problem?

Yes, the answer is correct, since 45 + 36 = 81.

There are eight friends at a party. If everyone at the party shakes hands with everyone else at the party, how many handshakes occur during the party?

Example 2

Think: Use a diagram to help you visualize the handshakes at this party.

A

B C D E F G H

If person A shakes hands with everyone in the room, 7 handshakes will occur.

Think: What happens when B starts to shake hands?

B

C D E F G H

There are 6 additional handshakes. Person C will

have 5 additional handshakes, and so on down to person G.

Think: How can the total of all handshakes be determined?

There are a total of 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 handshakes at this party.

Think: To check this answer, think back through the problem using the diagrams to make sure the answer is reasonable.

On a business trip Mr. Davis traveled by plane a total of 1,972 mi. The first leg of the trip was 561 mi., and the second leg was 749 mi. How long was the third leg of the trip?

Example

An athlete was running stairs. He would run half as many each time. If his first run was 120 stairs, how many stairs would he run by the time he was finished? (When he got to a half number, he went up a stair.)

Example

The three towns of Liberal, Dalhart, and Tucumcari are located in that order along a straight highway. The distance between Liberal and Dalhart is 114 mi. Tucumcari is located 93 mi. beyond Dalhart on the highway. How far is it from Liberal to Tucumcari?

Exercise

A ball made of special rubber compound was propelled 40 ft. into the air. Each time the ball hit the ground, it bounced half as high as its previous high point. How many times did the ball hit the ground before it bounced to a height of less than 2 ft.?

Exercise

During a busy period of time in a 25-story office building, an elevator started at the first floor, rose 2 floors, rose 9 floors, descended 6 floors, rose 8 floors, descended 5 floors, rose 6 floors, and descended 8 floors.

Exercise

On which floor was the elevator at the end of the period of time?

Exercise

If it takes the elevator 20 sec. to go from one floor to the next, how long was the elevator in motion?

Exercise

Twelve basketball teams will play in a tournament. Four will be given byes in the first round. They will be matched against the four first-round winners from the other eight teams. How many games will a team have to win in order to win the tournament?

Exercise

A spinner has four equally sized spaces on it numbered 1 through 4. If the spinner is spun twice, what are the possible sums that can be obtained? What sum occurs most often?

Exercise

Kellen and Sean start walking at the same time on the track. If Kellen can complete a lap in 3 min. and Sean can complete a lap in 4 min., how often will they cross the starting line together if they both walk for 30 min.?

Exercise

A picture frame is 2 in. wide and encloses a rectangular picture that has dimensions of 11 in. by 14 in. If the area of a rectangle is found by multiplying the length times the width, what is the area of the picture and frame together?

Exercise

The town of Palaski is 29 mi. south of Bixler. Grantville is 22 mi. north of Palaski. Philo is 18.5 mi. north of Grantville. What is the order of the towns from north to south?

Exercise

What is the distance between each town and the total distance from the town that is the farthest south to the town that is the farthest north?

Exercise