1 apple weighs x gram

1 banana weighs y gram; y> x
1 orange weighs z grams
A magician can combine 1 apple and one banana to make one orange. The magician is given 57 grams of apples and 57 grams of bananas. what is the theoretical yield? (i.e theoretically what is the mass of the oranges?

well, there are 57/y bananas

That means there must be only 57/y apples, so the result will be

57/y oranges, each having mass x+y

so, the mass of oranges will be

57(x+y)/y = 57(1+x/y) grams

To find the theoretical yield, we need to determine how many oranges can be created by combining the apples and bananas. We are given that 1 apple weighs "x" grams, 1 banana weighs "y" grams (where y > x), and 1 orange weighs "z" grams.

To determine the mass of the oranges, we can use the given information that the magician has 57 grams of both apples and bananas. We need to find the maximum number of oranges that can be created with this amount of fruit.

Let's assume we can create "n" oranges using 57 grams of apples and 57 grams of bananas.

The total mass of apples used in creating "n" oranges will be n * x grams.
The total mass of bananas used in creating "n" oranges will be n * y grams.

Since we are given that the magician has 57 grams of both apples and bananas, we can write the following equation:

n * x + n * y = 57

We know that 1 orange weighs "z" grams. Therefore, the total mass of "n" oranges will be n * z grams.

Since each orange is created by combining 1 apple and 1 banana, the total mass of oranges created should be equal to the total mass of apples and bananas used:

n * z = n * x + n * y

Now, we can substitute the given information: x = weight of apple, y = weight of banana.

Therefore, the theoretical yield, or the mass of the oranges, is n * z grams.