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Read a problem and make a plan


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Presentation Transcript
slide1

You run in a city where the short blocks on north-south streets are 0.1mile long. The long blocks on east-west streets are 0.15mile long. You will run 2 long blocks east, a number of short blocks south, 2long blocks west, then back to your starting point. You want to run 2miles. How many short blocks should you run?

EXAMPLE 1

Read a problem and make a plan

Running

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EXAMPLE 1

Read a problem and make a plan

SOLUTION

STEP 1

Read and Understand

What do you know ?

You know the length of each size block, the number of long blocks you will run, and the total distance you want to run.

You can conclude that you must run an even number of short blocks because you run the same number of short blocks in each direction.

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EXAMPLE 1

Read a problem and make a plan

What do you want to find out ?

You want to find out the number of short blocks you should run so that, along with the 4 long blocks, you run 2 miles.

STEP2

Make a Plan Use what you know to write a verbal modelthat represents what you want to find out. Then write an equation and solve it, as in Example2.

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Totaldistance(miles)

Length oflong block(miles/block)

Numbershort blocks(block)

Numberlong blocks(block)

Length ofshort blocks(miles/block)

+

=

0.1 s + 0.15 4 = 2

EXAMPLE 2

Solve a problem and look back

Solve the problem in Example 1 by carrying out the plan. Then check your answer.

SOLUTION

STEP 3

Solve the Problem. Write a verbal model. Then write an equation. Let sbe the number of short blocks you run.

The equation is0.1s + 0.6 = 2.One way to solve theequation is to use the strategy guess, check, and revise.

slide5

?

0.1(20) + 0.6 = 2

2.6 = 2

EXAMPLE 2

Solve a problem and look back

Guessan even number that is easily multiplied by0.1.Try20.Checkwhether20is a solution.

0.1s + 0.6 = 2

Write equation.

Substitute 20 for s.

Simplify; 20 does not check.

Revise.Because2.6 > 2, try an even number less than20.Try 14. Checkwhether14is a solution.

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?

0.1(14) + 0.6 = 2

2 = 2

ANSWER

To run2miles, you should run14short blocksalong with the4 long blocks you run.

EXAMPLE 2

Solve a problem and look back

0.1s + 0.6 = 2

Write equation.

Substitute 14 for s.

Simplify.

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EXAMPLE 2

Solve a problem and look back

STEP 4

Look Back Check your answer by making a table. You run0.6mile on long blocks. Each two short blocks add0.2mile.

The total distance is2miles when you run4long blocksand14short blocks. The answer in Step3 iscorrect.

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WHAT IF?In Example 1, suppose that you want to run a total distance of 3 miles. How many short blocks should you run?

for Examples 1 and 2

GUIDED PRACTICE

ANSWER

24short blocks