Sure, let's go through the problem step by step:
First, we need to understand the proportions given in the recipe:
- The recipe calls for [tex]\(1 \frac{1}{2}\)[/tex] cups of flour.
- The recipe also calls for [tex]\(\frac{3}{4}\)[/tex] of a stick of butter.
Jeremiah uses 3 sticks of butter. We need to determine how many cups of flour he will need if he uses 3 sticks of butter instead of [tex]\(\frac{3}{4}\)[/tex] of a stick.
1. Convert the mixed fraction [tex]\(1 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[
1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \text{ cups of flour}
\][/tex]
2. The original recipe's proportion can be described as:
[tex]\[
\frac{3}{2} \text{ cups of flour for } \frac{3}{4} \text{ stick of butter}
\][/tex]
3. We need to scale this proportion to account for 3 sticks of butter. Let [tex]\( x \)[/tex] be the amount of flour needed:
[tex]\[
\frac{3}{2} \text{ cups of flour} : \frac{3}{4} \text{ stick of butter} = x \text{ cups of flour} : 3 \text{ sticks of butter}
\][/tex]
4. Set up the proportion:
[tex]\[
\frac{3}{2} \div \frac{3}{4} = x \div 3
\][/tex]
5. To simplify the left side of the equation, recall that dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
\frac{3}{2} \times \frac{4}{3} = x \div 3
\][/tex]
6. Calculate the multiplication:
[tex]\[
\frac{3}{2} \times \frac{4}{3} = \frac{3 \times 4}{2 \times 3} = \frac{12}{6} = 2
\][/tex]
7. Now we have:
[tex]\[
2 = x \div 3
\][/tex]
8. Solve for [tex]\( x \)[/tex] by multiplying both sides by 3:
[tex]\[
x = 2 \times 3 = 6
\][/tex]
Thus, Jeremiah will need 6 cups of flour if he uses 3 sticks of butter.
The answer is:
(D) 6 cups
