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Chapter 3   

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Can Collectors

solution

Caryn filled 6 bags with 8 cans in each bag. She had a total of 48 cans.

Dexter filled 7 bags with 6 cans in each bag. He had a total of 42 cans.

Susie filled 5 bags with 9 cans in each bag. She had a total of 45 cans.

Vinny filled 6 bags with 7 cans in each bag. He had a total of 42 cans.

explanation

Step 1
1. Given: Total bags, 24 Dexter and Susie filled 12 bags. 24 total - 12 bags for Dexter and Susie = 12 bags left.
2. Therefore, that leaves 12 bags for Caryn and Vinny combined.
3. Given: Caryn and Vinny filled the same number of bags.
4. Since Caryn and Vinny combined filled 12 bags, they must have each filled 6.

Step 2
1. Given: Dexter had 2 more bags than Susie. Guess and check to make a list of combinations of 12, such as 11+1, 10+2, and so on.
2. Look for a combination where one digit is 2 more than the other. Result: 7+ 5 = 12

Step 3
Make a chart of facts known.

A data table

GUESS-AND-CHECK CHART #1
Guess the possible number of cans between 40 and 50 for the number of bags collected (a multiple of the number of bags). Then circle the final choice.

A data table

Step 4
Given: Dexter and Vinny have the same number of cans, so each has 42 cans.

Step 5
Add.
42 + 42 = 84

Step 6
Given: 177 cans in all.
Subtract to find out how many cans Caryn and Susie have combined:
177- 84 = 93

Together, Susie and Caryn collected 93 cans.

Step 6
Given: 177 cans in all.
Subtract to find out how many cans Caryn and Susie have combined:
177- 84 = 93
Together, Susie and Caryn collected 93 cans.

Step 7
Guess and Check:
Which combinations of cans total 93?
Look at Guess-and-Check Chart #1.
45 + 48 = 93

Step 8
Susie collected 45 cans.
Caryn collected 48 cans.

GUESS-AND-CHECK CHART #2
Use Steps 4, 7, and 8 to decide how many cans each person has.

A data table

A data table

 


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