Please help! Asap. U good in math cuz I'm not! Lol.

Mathematics

2 answers:

const2013 [10]3 years ago

5 0

Answer:

It depends.

4 for whole batches, \frac{16}{3} for partial batches.

Step-by-step explanation:

Let's assign variables. P for peanut butter, S for sugar, and E for egg.

According to the recipe, 1 batch is equivalent to:

$P=\frac{3}{4}\\S=1.5=\frac{3}{2}\\E=1$

I will give 2 responses. For one of the responses, I'll assume the question only wants a whole number of batches (which means no fractions or decimals). For the other, I'll assume that they accept parts of batches (i.e., accepts fractions and decimals).

If it's a whole number of batches, then it's pretty straight-forward. The main limiting factor would be whichever ingredient she has the least of.

Taking stock, she has $P=3\\S=9\\E=5\\$

To figure out which ingredient is the limiting factor, let's analyze each one individually. We'll assume that for each analysis, the other ingredients are in excess (meaning that we can make the max amount of batches possible based on just one of the ingredients).

Let's start with the eggs, since that's the simplest one. Since you need 1 egg for 1 batch, assuming the other ingredients are in excess, you can make 5 batches.

The sugar is also more or less simple, albeit not as much as the egg. It takes $\frac{3}{2}$ cups of sugar to make a batch. Molly has 9 cups available, so dividing 9 by $\frac{3}{2}$ will give us the amount of batches we can make based on the sugar, which turns out to be 6 batches.

$\frac{9}{\frac{3}{2}}\\\\9*\frac{2}{3} \\\\\frac{9}{3} *2\\\\3*2\\6$

For the peanut butter, we can use the same process. She has 3 cups available, and each batch needs $\frac{3}{4}$ of a cup. Dividing 3 by $\frac{3}{4}$ gives us a yield of 4 batches.

$\frac{3}{\frac{3}{4} }\\\\3*\frac{4}{3}\\\\\frac{3}{3} *4\\\\1*4\\4$

Of all the ingredients, the limiting factor is the peanut butter. So, Molly can only make 4 whole batches from her ingredients.

But what if we could make partial batches? Well then, that changes things a bit.

We would go through the calculations like normal, but there would also be an extra step. Since it takes 3 ingredients to make a batch, only having one of the ingredients would mean that we would have $\frac{1}{3}$ of a batch.