Question

Mito bakes biscuits. He uses 1/4 cup of flour to coat the countertop and the rillling pin. He also uses 2 1/2 cups of flour for each batch of biscuits he bakes. If he uses 7 3/4 cups of flour in all, how many batches of biscuits does he bake? Write and solve an equation.

Answer 1

Let \( x \) represent the number of batches of biscuits Mito bakes.

According to the problem, Mito uses:

- \( \frac{1}{4} \) cup of flour to coat the countertop and the rolling pin.
- \( 2 \frac{1}{2} = \frac{5}{2} \) cups of flour for each batch of biscuits.

The total amount of flour used is \( 7 \frac{3}{4} = \frac{31}{4} \) cups.

The equation to represent the total flour used is:

\[
\frac{1}{4} + x \cdot \frac{5}{2} = \frac{31}{4}
\]

Now, we need to solve for \( x \).

First, we can convert \( \frac{1}{4} \) to have a common denominator with \( \frac{31}{4} \):

\[
\frac{1}{4} = \frac{1}{4}
\]

Next, rewrite the equation:

\[
\frac{1}{4} + x \cdot \frac{5}{2} = \frac{31}{4}
\]

Subtract \( \frac{1}{4} \) from both sides:

\[
x \cdot \frac{5}{2} = \frac{31}{4} - \frac{1}{4}
\]

Calculating the right side:

\[
\frac{31}{4} - \frac{1}{4} = \frac{30}{4} = \frac{15}{2}
\]

Now, the equation simplifies to:

\[
x \cdot \frac{5}{2} = \frac{15}{2}
\]

To isolate \( x \), multiply both sides by the reciprocal of \( \frac{5}{2} \):

\[
x = \frac{15}{2} \div \frac{5}{2} = \frac{15}{2} \cdot \frac{2}{5} = \frac{15 \cdot 2}{2 \cdot 5} = \frac{15}{5} = 3
\]

Thus, Mito bakes \( \boxed{3} \) batches of biscuits.