Question

Lionel has at most 63/8 cups of flour to bake tortillas and a loaf of bread. Lionel uses 7/4 cups of flour to make the loaf of bread.

If each batch of tortillas takes 3/2 cups of flour, how many batches of tortillas, x, can Lionel bake? Select the inequality that includes the maximum number of batches of tortillas Lionel can bake.

Give me the answer is fraction form

Answer 1

To find out how many batches of tortillas Lionel can bake, we first need to determine how much flour he has left after using some for the bread.

Lionel has a total of \( \frac{63}{8} \) cups of flour. He uses \( \frac{7}{4} \) cups of flour for the loaf of bread.

First, convert \( \frac{7}{4} \) to have a common denominator with \( \frac{63}{8} \):

\[
\frac{7}{4} = \frac{7 \times 2}{4 \times 2} = \frac{14}{8}
\]

Now, subtract the amount of flour used for the bread from the total amount of flour:

\[
\text{Flour remaining} = \frac{63}{8} - \frac{14}{8} = \frac{63 - 14}{8} = \frac{49}{8}
\]

Next, each batch of tortillas takes \( \frac{3}{2} \) cups of flour. We can represent the number of batches of tortillas Lionel can bake, \( x \), using the following inequality:

\[
\frac{3}{2} x \leq \frac{49}{8}
\]

Now, to isolate \( x \), we multiply both sides of the inequality by the reciprocal of \( \frac{3}{2} \) (which is \( \frac{2}{3} \)):

\[
x \leq \frac{49}{8} \cdot \frac{2}{3}
\]

Calculating the right side:

\[
\frac{49 \times 2}{8 \times 3} = \frac{98}{24}
\]

Now simplify \( \frac{98}{24} \):

\[
\frac{98 \div 2}{24 \div 2} = \frac{49}{12}
\]

Thus, the inequality representing the maximum number of batches of tortillas \( x \) that Lionel can bake is:

\[
x \leq \frac{49}{12}
\]

Therefore, the answer in fraction form is:

\[
\boxed{\frac{49}{12}}
\]