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 weight with the peel?
Are you sure you don't mean that the unpeeled banana PLUS 7/8 oz. equals the weight of the unpeeled banana?
The problem does not make sense to me as stated. I assume that both bananas weighed the same before peeling. That is not made clear.
Let x be the banana's weight, in ounces.
7x/8 is the weight of the unpeeled banana.
Solve this equation:
7x/8 + 7/8 = x
To solve this problem, let's assume the weight of the unpeeled banana is represented by "x" ounces.
According to the given information, the banana peel weighs 1/8 the total weight of the banana. So, the weight of the banana peel is 1/8 * x = x/8 ounces.
Now, we know that the unpeeled banana balances a peeled banana of the same weight plus 7/8 of an ounce. This means the weight of the peeled banana is (x - x/8) + 7/8 = (7x - x)/8 + 7/8 = 6x/8 + 7/8 = 6x/8 + 7/8 = (6x + 7)/8 ounces.
Since the weight of the unpeeled banana balances the weight of the peeled banana plus 7/8 of an ounce, we can set up an equation:
x = (6x + 7)/8
To solve for x, we can cross-multiply:
8x = 6x + 7
Simplifying further:
8x - 6x = 7
2x = 7
x = 7/2
Therefore, the weight of the unpeeled banana (with the peel) is 7/2 ounces (or 3.5 ounces).
Let's assume the weight of the banana peel to be x ounces.
According to the given information, the weight of the banana peel is 1/8 of the total weight of the banana. Therefore, the weight of the banana (including its peel) is 8 times the weight of the peel.
So the weight of the banana (including its peel) is 8x ounces.
Now, we are also given that the weight of an unpeeled banana (8x ounces) balances a peeled banana of the same weight (8x ounces) plus 7/8 of an ounce.
Therefore, we can set up the equation:
8x = 8x + 7/8
To solve for x, we can simplify the equation:
8x - 8x = 7/8
0 = 7/8
Since the equation is contradictory (0 does not equal 7/8), there seems to be an error in the initial information provided. Please double-check the numbers and rephrase the question if necessary.