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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?

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Sep 13, 2010
College Algebra
by: Staff

The question:

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?

The answer:

This is simply 3 equations with 3 unknowns

1. Let:

P = weight of banana peel
U = weight of unpeeled banana
B = weight of peeled banana

2. Translate each part of the written problem into mathematical terms:


A banana peel weighs 1/8 the total weight of a banana.

P = (1/8) * U


A weight of a banana peel is also the difference between the weight of an unpeeled banana and the weight of a peeled banana

P = U – B


An unpeeled banana balances a peeled banana of the same weight plus 7/8 of an ounce

U = B + 7/8 oz


3. Now, solve the equations for U by substitution

P = (1/8) * U
P = U – B
U = B + 7/8 oz, stated another way: B = U – 7/8


Substitute U – B for the P in the first equation

P = (1/8) * U
U – B = (1/8) * U

Substitute U – 7/8 for the B

U – B = (1/8) * U
U – (U – 7/8 ) = (1/8) * U

Solve for U

U – (U – 7/8 ) = (1/8) * U
U – U + 7/8 = (1/8) * U
0 + 7/8 = (1/8) * U
7/8 = (1/8) * U
8*(7/8) = 8*(1/8) * U
7 = U

The final answer is: the weight of an unpeeled banana is 7 oz.



Of course, you could also begin by stating that the weight of a banana peel is 7/8 oz, and substitute the 7/8 for the P in equation 1.

P = (1/8) * U
7/8 = (1/8) * U
8*(7/8) = 8*(1/8) * U
7 = U




Thanks for writing.


Staff
www.solving-math-problems.com



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