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?

Let's assume that the weight of the unpeeled banana is "x" and the weight of the peeled banana is "y". According to the first statement, the weight of the banana peel is {eq}frac{1}{8} {/eq} of the total weight of the banana. Therefore, the weight of the peel can be expressed as {eq}xtimesfrac{1}{8}=frac{x}{8}. {/eq} According to the second statement, the unpeeled banana (which weighs "x") balances a peeled banana (which weighs "y") plus {eq}frac {7}{8} {/eq} of an ounce. This means that the weight of the unpeeled banana is equal to the weight of the peeled banana plus {eq}frac{7}{8}. {/eq} Therefore, we can express this relationship as: {eq}x=y+frac{7}{8}. {/eq} Now we can substitute the expression for the weight of the peel ({eq}frac{x}{8}{/eq}) into the equation above, since we know that the weight of the unpeeled banana includes the weight of the peel. This gives us: {eq}(y+frac{7}{8})=frac{x}{8}+y. {/eq} Simplifying this equation, we can cancel out the "y" terms and isolate "x": {eq}frac{x}{8}=frac{7}{8}. {/eq} Multiplying both sides by 8, we get: {eq}x=7. {/eq} So the unpeeled banana weighs 7 ounces. Finally, to find the weight of the banana with the peel, we can use the first statement again to calculate the weight of the peel: {eq}frac{x}{8}=frac{7}{8}div8=frac{7}{64}. {/eq} Adding this to the weight of the unpeeled banana, we get: {eq}7+frac{7}{64}=frac{455}{64}approx7.1. {/eq} Therefore, the weight of the banana with the peel is about 7.1 ounces.