Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 212

2
1
2
cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.(1 point)
cups

1 answer

Let \( F \) represent the amount of flour in the original recipe in cups. According to the information given:

In the original recipe for 4 loaves, the total amount of flour and sugar combined is:

\[ F + 2 \text{ (cups of sugar)} = \text{total amount of flour and sugar} \]

Kendra's adjusted recipe makes only 1 loaf and calls for \( 2 \frac{1}{2} \) cups of flour and sugar combined. We can also express \( 2 \frac{1}{2} \) cups as a proper fraction:

\[ 2 \frac{1}{2} = \frac{5}{2} \text{ cups} \]

Since Kendra is making just one loaf, we can set up the following proportion based on the fact that the original recipe makes 4 loaves, thus:

\[ \frac{1}{4} \times (F + 2) = \frac{5}{2} \]

To find \( F \), we first multiply both sides by 4:

\[ F + 2 = 4 \times \frac{5}{2} \]

Calculating the right side:

\[ 4 \times \frac{5}{2} = 2 \times 5 = 10 \]

Now we have:

\[ F + 2 = 10 \]

Subtracting 2 from both sides gives:

\[ F = 10 - 2 = 8 \]

Thus, the amount of flour in the original recipe is \( \boxed{8} \) cups.