Math 7 (Period 4)

Problem Solving Strategies 4.6

WORD PROBLEMS! YAY!

Often there are several ways to solve a real-life problem It can be helpful to use more than one method and then compare results…

We turned to the textbook Page 193 and looked at the Example 1 problem…

A logging company is making a reforestation plan. The company has 90 square miles of logged land and is logging 15 square miles more each year. The company plants 30 square miles f new trees each year.

Predict how long it will take for the logged land to be reforested.

Method 1

You can use a table and look for a pattern For the logged land start with 90 square miles and add 15 square miles each year. For the reforested land, start at 0 (because they hadn’t started this program, yet) and add 30 square miles each year.

See the chart:

Year	0 (NOW)	1	2	3	4	5	6
Logged land ( in square miles)	90	105	120	135	150	165	180
Reforested (in square miles)	0	30	60	90	120	150	180

From the table you can see that will take 6 years to reforest all the and that has been logged.

Method 2

Please turn to page 193 and look at the coordinate graph to visualize the same data as in the table above. That graph shows that the amount of reforested land steadily approaches the amount of logged land. It also shows that it will take 6 years to reforest the logged land.

Method 3

Use an equation to solve this problem

Please look at Page 194 for the Verbal Model

   

We know:                                                                    

Land already logged = 90

Land logged per year = 15

Number of years= THAT”S WHAT WE DON”T KNOW!

Let n = the number of years

Land reforested per year = 30

90 + 15n = 30n

NOW we can solve the equation

subtract 15n from both sides

90 = 15n

90/15 = 15n/15

6 = n

So it will take 6 years to reforest all the logged land!

MOVIES

Suppose the cost of seeing a movie at a theater is $7. Buying a DVD player costs  $360 and renting a movie to use on the DVD player is $4.

Write an expression to represent the cost of seeing y movies at a theatre… and write an expression to represent the cost of renting the same number of movies to use on your DVD player ( include the cost of the DVD player)

7y = the cost at the theater

360 + 4y = the cost at home

How many moves must you see so that the  two costs are the same? Write an equation that models that situation and solve for y- the number of movies watched.

7y = 360 + 4y

3y = 360

y =120

You would need to watch 120 movies to have the cost the SAME!

Suppose you watched more than 120 movies… which would cost less at that point… going to the theatre or renting DVD movies?

Renting DVD movies. The cost is only $4 for a DVD  and it is $7 at the theater.

Aesop’s Fables

In one of Aesop’s Fables, a tortoise and a hare are in a race. The hare is far ahead and SURE to win, so it takes a nap. When the hare wakes up, it sees that the tortoise is about to cross the finish line.

Suppose the hare runs 600 inches per second and the tortoise runs 3 inches per second. When the hare wakes up, the tortoise is 1000 feet (12,000 inches) ahead. Which equation represents when the hare will catch up with the tortoise? (Hint: If t represents time in seconds, then 3t is the distance in inches the tortoise can  travel in t seconds…)

A.  3t = 600t  +  12,000            B. 600t = 3t + 12,000

C. 3t – 12000 = 600t                 D. 600t = 12,000

We had a class discussion on Wednesday about the correct equation—which is B.

Using 600t = 3t + 12, 000, we solved for t

and discussed what our solution meant.

597t = 12,000

597t/597 = 12,000/597

t =20.1

20.1 seconds is the time when the hare will catch up with the tortoise.

If the tortoise is 5 feet (60 inches) from the finish line when the hare wakes up, who will win the race? Explain…