6th Grade Math Textbook, Fundamentals

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Problem-Solving Strategy:

Guess and Test

Objective To solve problems using the strategy Guess and Test

Problem 1: Exactly 440 tickets to a play were sold. Seats were
priced at only two levels: $18 or $10. The total revenue on
tickets sales was $6640. How many $18 tickets were sold?

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Read to understand what is being asked.

List the facts and restate the question.

Facts: Some tickets sold for $18, others for $10.

There were 440 tickets sold in all.

The combined value of all tickets sold

was $6640.

Question:How many $18 tickets were sold?

Select a strategy.

Since there are a finite number of possibilities,

you can try to find the solution by using the

strategy Guess and Test.

Apply the strategy.

Begin by guessing that half of the tickets (that is,

• 440 tickets 220 tickets) were $18 tickets and
  the other half were $10 tickets.
  Calculate the revenue for all the tickets:
  220 • $18 220 • $10 $6160
  This is less than the actual revenue of $6640. So adjust the guess,
  increasing the number of $18 tickets, and calculate the revenue again.
  Continue guessing, testing, and adjusting until you get the correct answer.
  Make a table like the one below to keep track of the results.

So 280 of the $18 tickets were sold.

Number $18 Tickets Number $10 Tickets Revenue Comment

220 220 $6160 Too low; try more $18 tickets.

300 140 $6800 Too high; the number of $18 ticketsmust be between 220 and 300.

260 180 $6480 Too low; the number of $18 ticketsmust be between 260 and 300.

280 160 $6640 Correct!

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2

Check to make sure your answer makes sense.

If 280 tickets were sold at $18 each, it would generate 280 • $18,

or $5040, in revenue.

The remaining tickets (440 280, or 160), sold for $10 each,

provide additional revenue of 160 • $10, or $1600.

Therefore, the total revenue is $5040 $1600, or $6640.

Problem-Solving Strategies

1.Guess and Test

2.Organize Data

3.Find a Pattern

4.Make a Drawing

5.Solve a Simpler Problem

6.Reason Logically

7.Adopt a Different Point of View

8.Account for All Possibilities

9.Work Backward

10.Consider Extreme Cases