# 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.

**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.

### 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 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.