To find out how many cups of almonds Luis needs when using 3 cups of chocolate chips, we can set up a proportion based on the original recipe.
The recipe states that for every \( \frac{1}{2} \) cup of almonds, \( \frac{3}{4} \) cup of chocolate chips is used.
First, we will express the amounts in a ratio:
\[ \text{Almonds} : \text{Chocolate Chips} = \frac{1}{2} : \frac{3}{4} \]
To use this ratio properly, we can convert it into a simpler form. To compare the proportions, we can multiply both sides by a common denominator; in this case, we could multiply the ratio by 4 to eliminate the fractions:
\[ \text{Almonds} : \text{Chocolate Chips} = 2 : 3 \]
This means that for every 2 cups of almonds, 3 cups of chocolate chips are used.
Now, if Luis uses 3 cups of chocolate chips, we can set up the following proportion to find the required amount of almonds (let \( x \) be the amount of almonds):
\[ \frac{2}{3} = \frac{x}{3} \]
To solve for \( x \), we can cross-multiply:
\[ 2 \times 3 = 3 \times x \]
This simplifies to:
\[ 6 = 3x \]
Now, divide both sides by 3:
\[ x = 2 \]
So, Luis will need 2 cups of almonds for 3 cups of chocolate chips.
To summarize, if Luis uses 3 cups of chocolate chips, he will need 2 cups of almonds.
None of the options listed (0.4, 0.5, 0.8, 18.0) are correct based on the calculations done above.