Use Multiple Strategies

ExampleMr. Tirado has boxes that measure 20” × 13” × 9” high. He wants to store them in a room 12’ × 10’ × 9’. If he stacks the boxes side by side and on top of each other but cannot stack the boxes on their sides, how many boxes can he store in this room?

Think: How can you organize this information to find the number of boxes? Would a picture help? Would it help to solve a simper problem first? How many boxes will fit in one layer on the floor of the room?

Convert the dimensions of the floor into inches and draw a diagram.

12 ft. = 144 in. long10 ft. = 120 in. wide

144 in.

120 in.

Think: How could the boxes fit into the room? Should the length of the boxes be placed along the length of the room or the width? What operation should be used to determine the number of boxes that can be place lengthwise along the length of the room?

Divide the length of a box into the length of the room to determine how many boxes one layer deep can fit in the room.

144 ÷ 20 = 7.2

Seven boxes can be placed along the length of the room. There will be 4 in. of space at one end of the room.

Think: How many boxes will fit this way on the floor if the width of a box is 13 in. and the width of the room is 120 in.?

120 ÷ 13 = 9.23

Nine boxes will fit along the width of the room. There will be 3 in. of space on one side of the room.

Think: How many boxes will fit on the floor of the room?

7(9) = 63If the boxes are placed in the room in this manner, there will be 63 boxes per layer with little wasted space.

144 in.

120 in.

Think: How high can the boxes be stacked?

The room, is 9 ft. high, which is 108 in. tall, so a stack of exactly 12 layers of boxes should fit into the room, assuming the door allows you to stack them all the way to the ceiling.

Think: How many boxes can be stored in the room in this configuration?

63(12) = 756 boxes can be stored in the room.

Think: Is this the most efficient way to use the room? Is there any way more boxes could be stored in the room? What problem-solving processes were used to solve this problem?

There is little wasted space in this configuration. This seems to be very efficient. Several processes were used, including drawing a diagram, selecting correct operations, and guess and check.

Use the information in the example problem and determine how many boxes could be placed in the room if the length of each box were placed along the width of the room.

Exercise

How many inches of space are wasted in each direction? Which method allows more boxes to be stored?

Exercise

144 in.

120 in.

792; 1” along length only;

this method

A shop had 72 bicycles with a price tag of $149.95. Before Christmas, the shop reduced the price by $32.99 and sold 49 of them. The rest were sold at the original price. How much money did the shop receive from the sale of all 72 bicycles?

Exercise

$9,179.89

The Kingsbury Middle School eight-grade, is planning a class trip to an amusement park. There are 174 students in the eighth grade, and the total cost of the trip is $7,482. This amount includes the total cost of admission to the park and $870 for transportation.

Exercise

How much is admission for each student; how much will each student have to pay to cover the bus expenses; and what is the total cost for each student?

Exercise

$38 admission fee; $5 bus fee; $43 total

One family has six members who all give Christmas gifts to one another. If they have been doing this for eight years, how many gifts have been exchanged?

240 gifts

Exercise

If they have a $10 price limit on the gifts, what is the maximum amount of money spent by the family members over those eight years?

Exercise

$2,400

Sarah watches the temperature of a solution during a science experiment. She is to allow the solution to cool and heat several times throughout the project. The first reading is half the temperature of the final reading.

Exercise

During the experiment the solution’s temperature rises 12°, falls 4°, rises 33°, falls 11°, and rises 26°. What are the initial and final temperatures of the solution?

Exercise

initial: 56°; final: 112°

The house numbers along the south side of Elm Street are numbered by consecutive odd numbers. The first number on the block is 201. If the last number on the block is 231, how many houses are on the south side of Elm Street in the block? 16 houses

Exercise

Mrs. Koto drives her car at an average speed of 48 mi./hr. for 30 min. and then increases her speed to an average of 64 mi./hr. for 2 hr. to arrive at her daughter’s house.

Exercise

If she is slowed down on the way home along the same route and it takes her 4 hr. to get home, what is her average speed on the way home?

Exercise

38 mi./hr.

A soda can display has 105 cans. There is one fewer can in each row than in the row below, with a single can in the top row.

Exercise

How many cans are in the bottom row? How many rows are there? If each soda can is 5 in. tall, how high does the display reach?

Exercise

bottom: 14 cans; 14 rows; 70 in. high