Math  /  Algebra

Question44 \mid Your dad uses 5 cups of apples for every 2 cups of sugar to make apple pie. If he wanted to make more pies using 8 cups of apples, how many cups of sugar would he need?

Studdy Solution

STEP 1

What is this asking? How many cups of sugar do we need if we use 8 cups of apples, keeping the same ratio as before? Watch out! Don't mix up the ratio of apples to sugar!
Keep the relationship the same.

STEP 2

1. Understand the ratio
2. Set up the proportion
3. Solve for sugar

STEP 3

Alright, let's get this straight!
The original recipe uses **5 cups of apples** for every **2 cups of sugar**.
This means the ratio of apples to sugar is 52 \frac{5}{2} .

STEP 4

This ratio tells us how many cups of sugar we need for any given number of cups of apples.
It's like the secret formula for the perfect pie!

STEP 5

Now, we want to make more pies with **8 cups of apples**.
So, let's set up a proportion to find out how many cups of sugar we need.

STEP 6

We can write the proportion as:
52=8x\frac{5}{2} = \frac{8}{x}
where x x is the number of cups of sugar we need.
This equation keeps the ratio the same!

STEP 7

To solve for x x , we need to **cross-multiply**.
This means we'll multiply the numbers diagonally across the equal sign.
So, we have:
5x=285 \cdot x = 2 \cdot 8

STEP 8

Let's do the math!
Multiply both sides:
5x=165x = 16

STEP 9

Now, we need to **divide to one** to solve for x x .
Divide both sides by 5:
x=165x = \frac{16}{5}

STEP 10

And when we do the division, we find:
x=3.2x = 3.2
So, we need **3.2 cups of sugar**!

STEP 11

To make pies using **8 cups of apples**, your dad needs **3.2 cups of sugar**.

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