PRE-ALGEBRA

PRE-ALGEBRA

Lesson 2-7 Warm-Up

PRE-ALGEBRA

Reasoning Strategy: Try, Test,Revise (2-7)

Sometimes, it might be necessary to try a conjecture, test your conjecture, and if it isn’t correct, use what you learned to make a better conjecture the next time.Example: The drama club put on a play. For the first performance, the club sold 133 tickets and raised $471. Tickets cost $4 for adults and $3 for students. How many student and adult tickets did the club sell?

The drama club sold 72 adult and 61 student.

Example: Steven has $2.30 all in quarters and nickels. He has four more nickels than quarters. How many nickels and quarters does Steven have?

Steven has11 nickels and 7 quarters.

Adult Tickets Student Tickets Total $

60 133 – 60 = 73 60 ($4) + 73($3) = $240 + $219 = $459 (too low)

80 133 – 80 = 53 80 ($4) + 53($3) = $320 + $159 = $479 (too high)

70 133 – 70 = 63 70 ($4) + 63($3) = $280 + $189 = $469 (a little too low)

72 133 – 72 = 61 72 ($4) + 61($3) = $288 + $183 = $471 (correct)

Nickels Quarters Total $14 10 14 ($0.05)+ 10 ($0.25) =$0.70 + $2.50 = $3.20 (too high)

9 5 9($0.05) + 5($0.25)= $0.45 + $1.25 = $1.70 (too low)

12 8 12($0.05) + 8 ($0.25) = $0.60 + $2.00 = $2.60 (a little high)

11 7 11($0.05) + 7 ($0.25) = $0.55 + $1.75 = $2.30 (correct)

How do you use the “try, test, and revise” strategy?

PRE-ALGEBRA

During the intermission of the play, the Theater Club sold

cups of popcorn and soda. The club sold 79 cups of popcorn and

96 sodas for a total of $271. What was the selling price of a cup of

popcorn? Of a soda?

You can organize conjectures in a table. As a first conjecture, try both with a price of $1.

Reasoning Strategy: Try, Test, ReviseLESSON 2-7

Additional Examples

PRE-ALGEBRA

(continued)

Popcorn SodaPrice Price Total Price

$1 $1 79(1) + 96(1) = 79 + 96 The total is too low. Increase = 175 the price of the popcorn only.

$2 $1 79(2) + 96(1) = 158 + 96 The total is too low. = 254 Increase the price of the soda.

$2 $2 79(2) + 96(2) = 158 + 192 The total is too high. = 350 Decrease the price of the popcorn.

$1 $2 79(1) + 96(2) = 79 + 192 The total is correct. = 271

The popcorn price was $1, and the soda price was $2.

Reasoning Strategy: Try, Test, ReviseLESSON 2-7

Additional Examples

PRE-ALGEBRA

Solve using any strategy.

1. A sporting goods store manager ordered twice as many pairs of basketball shoes as tennis shoes. He ordered 96 pairs in all. How many pairs of each did he order?

2. Manuel wrote a 512-word paper over the weekend. He wrote 180 more words on Sunday than he did on Saturday. How many wordsdid he write on Saturday?

166

32 pairs of tennis shoes; 64 pairs of basketball shoes

Lesson Quiz

Reasoning Strategy: Try, Test, ReviseLESSON 2-7