Bananas!
Introduction
In this unit we first present a word problem, and then we check how realistic the problem is by carrying out a small experiment.
Billstein, Libeskind, and Lott, in their book Mathematics for Elementary School Teachers, quote the following word problem from "Peanuts" by Charles Schulz.


A young girl is reading a word problem in class:
"A banana peel weighs 1/8 the total weight of a banana."
"If an unpeeled banana balances a peeled banana of the same weight plus 7/8 of an ounce, ..."
" ... how much does the banana weigh with peel?"

She shouts: "ABANDON SHIP!!!"


Here is an algebraic solution.
Let
b be the weight of an unpeeled banana (in ounces), and
p be the weight of its peel;
so
b - p is the weight of a peeled banana (the edible part).


We know that
p = (1/8)*b = b/8, and
b = (b - p) + 7/8 = b - p + 7/8.

Thus,
b - b + p = 7/8,
p = 7/8, b/8 = 7/8, b = 7.

Therefore, the whole banana weighs 7 ounces; its peel weighs 7/8 ounces; and the peeled banana (the edible part) weighs 6 1/8 ounces.


This means that 6.125/7 of the weight of the banana, or 7/8, or 87.5%, is in the peeled banana, and .875/7 of the weight of the banana, or 1/8, or 12.5%, is in the peel. How realistic is this? Try the activity in the next section to find out!
Activity
What percentage of the weight of a banana is the edible part? What percentage of the weight is the peel?

Supplies: Students work in groups. Each group needs one whole banana (with peel), scales, plastic ziplock bag, and calculator

1. Estimation
Children should first estimate the percentage of the weight of their banana that is contained in the edible part. These estimates should be written down.

2. Weighing and computing the percentage of weight contained in the edible part
a. Weigh the banana; write down the weight.

b. Peel the banana and put the edible part in a ziplock bag.

c. Weigh the edible part and the peel together; check that it is the same as in (a).

d. Weigh the edible part alone and write down the weight.

e. Weigh the peel and write down the weight. Check that weight of peel plus weight of edible part equals total weight.

f. The percentage of the weight contained in the edible part is (weight of edible part / weight of whole banana)*100.

Calculator button presses:
[weight of edible part] [/] [weight of whole banana] [%]

or

[weight of edible part] [/] [weight of whole banana] [*] [100] [=]


Our banana weighed 4 3/4 ounces, or 4.75 oz.
The peel weighed 1 3/4 oz, and the edible part weighed 3 oz.
Button Presses: Display:
[3][/][4.75][%] 63.157894
The edible part of the banana is only 63% of the weight! That is only slightly more than 5/8 of the weight (5/8 = .625), not 7/8 as in the word problem above.

g. The percentages from all groups should be written in a table on the board. A discussion should follow. How did the estimates compare with the actual percentage?
3. Related topics
a. How much does a banana cost?
We paid 44 cents per pound for our banana.
4 3/4 ounces is 4.75/16 = 0.296875 lb.
Button Presses: Display:
[.44] [*] [0.296875] [=] 0.130625
Our banana cost about 13 cents.

b. How much does the peel of a banana cost?
Our banana peel weighed 1 3/4 ounces.
Button Presses: Display:
[.44] [*] [1.75] [/] [16] [=] 0.048124
The peel cost nearly five cents.

c. How would the price of the banana change if the price per pound was 59 cents?

d. What percentage of the weight of an orange is the edible part?



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