Backpack Weigh-In

Solution

Elena: 19.8 lb
Joe: 19.35 lb
Owen: 18.9 lb
Samantha: 18.05 lb
Tuck: 19.5 lb

Explanation

Step 1

List the weights from lightest to heaviest. It may be useful to list each weight to the hundredths place.

18.05 = 18.05 lb
18.9  = 18.90 lb
19.35 = 19.35 lb
19.5  = 19.50 lb
19.8  = 19.80 lb

Step 2

Rule out the impossibilities.
(Put an X in the boxes that you rule out.)

Elena's Backpack
Since Elena's backpack weighs the most, it must weigh 19.8 lb.

Samantha's Backpack
To find the weight of Samantha's backpack, add the weight of her lunch to the weight of the backpack without lunch.

 1.5   lb (weight of lunch) +16.55 lb (weight of backpack without lunch) 18.05 lb (weight of Samantha's backpack)

Owen's, Joe's, and Tuck's Backpacks
Owen's backpack is 0.45 lb less than Joe's. Subtract 0.45 lb from the remaining three weights to find a difference equal to another backpack weight.

 19.50 lb − 0.45 lb 19.05 lb
 19.35 lb − 0.45 lb 18.90 lb
 18.90 lb − 0.45 lb 18.45 lb
None of the backpacks weighs this amount. The fifth backpack weighs this amount. None of the backpacks weighs this amount.

Based on the above information, Joe's backpack weighs 19.35 lb and Owen's backpack weighs 18.9 lb. There is a difference of 0.45 lb between them. The remaining backpack, which weighs 19.5 lb, belongs to Tuck.

Step 3

Use this chart to rule out the impossibilities.

18.05 18.90 19.35 19.50 19.80 X X X X yes X X yes X X X yes X X X yes X X X X X X X only one left X