GUESS+AND+CHECK

Guess and Check

Question: Amy and Judy sold 12 show tickets altogether. Amy sold 2 more tickets than Judy. How many tickets did each girl sell?

Strategy:

1) UNDERSTAND:

What do you need to find?

You need to know that 12 tickets were sold in all. You also need to know that Amy sold 2 more tickets than Judy.

2) PLAN:

How can you solve the problem?

You can guess and check to find two numbers with a sum of 12 and a difference of 2. If your first guess does not work, try two different numbers.

3) SOLVE:

First Guess: Amy = 8 tickets Judy = 4 tickets

Check 8 + 4 = 12 8 - 4 = 4 ( Amy sold 4 more tickets) <span style="font-family: Georgia,serif; font-size: 140%;">These numbers do not work!

<span style="font-family: Georgia,serif; font-size: 140%;">Second Guess: <span style="font-family: Georgia,serif; font-size: 140%;">Amy = 7 tickets <span style="font-family: Georgia,serif; font-size: 140%;">Judy = 5 tickets

<span style="font-family: Georgia,serif; font-size: 140%;">Check <span style="font-family: Georgia,serif; font-size: 140%;">7 + 5 = 12 <span style="font-family: Georgia,serif; font-size: 140%;">7- 5 = 2 ( Amy sold 2 more tickets) <span style="font-family: Georgia,serif; font-size: 140%;">These numbers do work!

<span style="font-family: Georgia,serif; font-size: 140%;">Amy sold 7 tickets and Judy sold 5 tickets.

<span style="font-family: Georgia,serif; font-size: 140%;">LEARN ABOUT IT <span style="font-family: Georgia,serif; font-size: 140%;">Some problems cannot be solved directly. You need to use a strategy called Guess and Check. <span style="font-family: Georgia,serif; font-size: 140%;">Prince Carl divided 15 stone games into two piles: games he owns and games his brother owns. He owns 3 more games than his brother. How many games does his brother own? <span style="font-family: Georgia,serif; font-size: 140%;">
 * <span style="font-family: Georgia,serif; font-size: 140%;">I'll guess his brother owns 8 games.
 * <span style="font-family: Georgia,serif; font-size: 140%;">That means Prince Carl owns 11 games. That's a total of 19 games.
 * <span style="font-family: Georgia,serif; font-size: 140%;">My guess is too high.
 * <span style="font-family: Georgia,serif; font-size: 140%;">I'll guess again. This time I'll guess his brother owns 6 games.
 * <span style="font-family: Georgia,serif; font-size: 140%;">That means Prince Carl owns 9 games. That's a total of 15 games.
 * <span style="font-family: Georgia,serif; font-size: 140%;">My guess is right.
 * <span style="font-family: Georgia,serif; font-size: 140%;">His brother owns 6 games.