A recipe calls for 13

Question

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:

$$3÷52\approx 0.0576923077.$$

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:

$$\boxed{{\displaystyle 0.0576923077}}.$$

Or approximately $0.058$ if rounding to three decimal places.