Question

A recipe calls for 13
teaspoon of salt and 34
cup of flour. To maintain the ratio, how many cups of flour should be mixed with 1 teaspoon of salt? Express the answer in exact decimal form.(1 point)
cups of flour

Answer 1

To maintain the ratio of salt to flour, we start with the given amounts from the recipe, which are \( \frac{13}{1} \) teaspoons of salt to \( \frac{3}{4} \) cup of flour.

First, we convert \( \frac{3}{4} \) cup of flour to a decimal:

\[
\frac{3}{4} = 0.75 \text{ cups of flour.}
\]

Now we can express the ratio of salt to flour:

\[
\text{Ratio} = \frac{13 \text{ teaspoons of salt}}{0.75 \text{ cups of flour}}.
\]

To find out how many cups of flour correspond to 1 teaspoon of salt, we set up a proportion based on the existing ratio:

Let \( x \) be the amount of flour (in cups) that corresponds to 1 teaspoon of salt. The ratio can be set up as follows:

\[
\frac{13}{0.75} = \frac{1}{x}.
\]

Cross multiplying gives:

\[
13x = 0.75.
\]

Now, solving for \( x \):

\[
x = \frac{0.75}{13}.
\]

Calculating \( \frac{0.75}{13} \):

First, convert \( 0.75 \) to a fraction:
\[
0.75 = \frac{3}{4}.
\]

Now substitute:
\[
x = \frac{3/4}{13} = \frac{3}{4 \times 13} = \frac{3}{52}.
\]

Now, converting \( \frac{3}{52} \) to decimal format:

\[
3 \div 52 \approx 0.0576923077.
\]

Rounding to an appropriate number of significant figures (as needed), we find:

\[
x \approx 0.0577.
\]

Thus, the exact decimal form of cups of flour to mix with 1 teaspoon of salt is:

\[
\boxed{0.0576923077}.
\]

Or approximately \( 0.058 \) if rounding to three decimal places.