Package Pile

Solution

Box	Box 1	Box 2	Box 3	Box 4	Box 5
Person	Curtis	Trevor	Driscoll	Lori	Amanda
Volume	V = 1,485 in.³	V = 1,440 in.³	V = 2,340 in.³	V = 1,404 in.³	V = 1,428 in.³

Explanation

Step 1

Find the height of Box 2.

The clue given: They have piled them into a stack 43 inches high.
Add to find the total height of the other boxes: 9 in. + 10 in. + 9 in. + 7 in. = 35 in.
Subtract: 43 in. − 35 in. = 8 in.
Box 2 is 8 inches high.

Step 2

Find the volume of each box.
Use the formula: V= l x w x h

Box 1
V = 15 in. x 11 in. x 9 in.
V = 1,485 in.³

Box 2
V = 15 in. x 12 in. x 8 in.
V = 1,440 in.³

Box 3
V = 18 in. x 13 in. x 10 in.
V = 2,340 in.³

Box 4
V = 13 in. x 12 in. x 9 in.
V = 1,404 in.³

Box 5
V = 17 in. x 12 in. x 7 in.
V = 1,428 in.³

Box 1	Box 2	Box 3	Box 4	Box 5
l = 15 in. w = 11 in. h = 9 in.	l = 15 in. w = 12 in. h = ?	l = 18 in. w = 13 in. h = 10 in.	l = 13 in. w = 12 in. h = 9 in.	l = 17 in. w = 12 in. h = 7 in.
V = 1,485 in.³	V = 1,440 in.³	V = 2,340 in.³	V = 1,404 in.³	V = 1,428 in.³

Step 3

Use the clues to find out who packed each box.

The volume of Lori's box is the least.
The volume of Box 4 is 1,404 in.³ It has the least volume.
Driscoll's box has the greatest volume.
Box 3 has the greatest volume with 2,340 in.³
The volume of Amanda's box is less than Trevor's box.
Amanda's box could be Box 2 or Box 5. Look at the next clue.
The box Curtis filled has a greater volume than Trevor's box.
Since Amanda's has less volume than Trevor's, and Trevor's has less volume than Curtis's box, then Amanda's box has to have less volume than both.

That means the following:
The least volume of the 3, Box 5, with a volume of 1,428 in.³ was filled by Amanda.
Trevor filled the box with the next least volume of the three, Box 2, with a volume of 1,440 in.³
Curtis filled the box with the greatest volume of the 3, Box 1, with a volume of 1,485 in.³

Curtis	Trevor	Driscoll	Lori	Amanda
Box 1	Box 2	Box 3	Box 4	Box 5
V = 1,485 in.³	V = 1,440 in.³	V = 2,340 in.³	V = 1,404 in.³	V = 1,428 in.³