The Price is Right
- Imagine that our class has been asked to work with a local non-profit business to ship Brain Boxes to a school in Honduras. The business will provide the Brain Erasers and the small boxes to put each Brain Eraser in. Each receiving student would get one Brain Box. It will be our job to raise the money for shipping the Brain Boxes to the American Embassy in Honduras for distribution to schools, packing the boxes, and taking them to the post office for shipping.
- Before we can solicit donations for shipping (our goal is to collect $100) we need to develop a plan for shipping so that we can ship the most amount of Brain Boxes for the least amount of money.
- The Brain boxes are rectangular prisms with the dimensions 1 ¼” x 1 ¼” x 1 ¼”
- The U. S. Postal Service has Flat Rate boxes that ship for specific amounts no matter how much the box weighs.The inside* dimensions of the boxes are:
Small Box ($5.80) 8 5/8” x 5 3/8” x 1 5/8”
Medium Box #1 ($12.35) 11” x 8 ½” x 5 ½”
Medium Box # 2 ($12.35) 13 5/8” x 11 7/8” x 3”
Large Box ($16.85) 12” x 12” x 5 ½”
- Your job is to find which “price is right” meaning, which box would ship the most amount of Brain Boxes for the least unit price?
- Explain your plan using mathematical calculations, illustrations, and words.
* The measurements given are inside dimensions of the boxes, not the actual sizes of the boxes. We need the inside measurements because we’re placing the Brain Boxes inside the shipping boxes. The outside measurements would include the actual construction material of the boxes.
The Price is Right
Answer Key
Small Box Calculations
Small Box ($5.80) 8 5/8” x 5 3/8” x 1 5/8”
Brain Box 1 ¼” x 1 ¼” x 1 ¼”
First calculate 8 5/8” 1 ¼” = 6.9 (6 boxes)
Next, calculate 5 3/8” 1 ¼” = 4.3 (4 boxes)
With a height of 1 5/8” we can only stack one row of boxes. The row will be 6 boxes across and 4 boxes wide so the Small box will ship 24 boxes.
The cost of the Small Box is $5.80.
Calculate $5.80 24 = $0.2416; rounded to the nearest cent = $0.24
Using the Small box, it will cost $0.24 per Brain Box to ship.
Medium Box # 1 Calculations
Medium Box # 1 ($12.35) 11” x 8 ½” x 5 ½”
Brain Box 1 ¼” x 1 ¼” x 1 ¼”
Calculate 11” 1 ¼” = 8.8 (8 boxes)
Calculate 8 ½” 1 ¼” = 6.8 (6 boxes)
Calculate 5 ½” 1 ¼” = 4.4 (4 boxes)
Multiply 8 x 6 x 4 + = 192
Calculate $12.35 192 = $0.0643 ($0.06)
Using Medium Box # 1, it will cost $0.06 per Brain Box to ship.
Medium Box # 2 Calculations
Following the steps above you will find that it costs $0.0457 ($0.05) per Brain Box to ship.
Large Box
Following the steps above you will find it costs $0.0520 ($0.05) per Brain Box to ship.
Teaching Note
Students will at this point notice that it’s the same unit price for the medium box #2 and the large box. Encourage your students to calculate the price for shipping multiple boxes and see if it makes a difference in unit pricing.
Example:
• To ship 8 medium box # 4 it would cost $98 to ship 2160 Brain Boxes @ a cost of $0.0453 per box.
• To ship 6 large boxes it would cost $101.10 to ship 1944 Brain Boxes @ a cost of $0.052 per box.
So…it now appears that our best price is to ship 8 boxes of Medium Box # 4!