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### 2.3: Making Bread Dough

A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of honey to flour. Complete the table as you answer the questions. Be prepared to explain your reasoning.

1. How many cups of flour do they use with 20 tablespoons of honey?
2. How many cups of flour do they use with 13 tablespoons of honey?
3. How many tablespoons of honey do they use with 20 cups of flour?

\[
\begin{tabular}{|l|l|}
\hline
honey (tbsp) & flour (c) \\
\hline
8 & 10 \\
\hline
20 & \\
\hline
13 & \\
\hline
& 20 \\
\hline
\end{tabular}
\]

Answer :

Sure! Let's work through each part of the problem step-by-step.

### Step-by-Step Solution:

The bakery uses a ratio of 8 tablespoons of honey for every 10 cups of flour. This ratio can be written as:
[tex]\[ \frac{8 \, \text{tbsp honey}}{10 \, \text{cups flour}} \][/tex]

#### 1. How many cups of flour do they use with 20 tablespoons of honey?

To find this, we set up a proportion based on the given ratio:
[tex]\[ \frac{8 \, \text{tbsp honey}}{10 \, \text{cups flour}} = \frac{20 \, \text{tbsp honey}}{x \, \text{cups flour}} \][/tex]

Cross-multiplying to solve for [tex]\( x \)[/tex]:
[tex]\[ 8x = 20 \times 10 \][/tex]
[tex]\[ 8x = 200 \][/tex]
[tex]\[ x = \frac{200}{8} \][/tex]
[tex]\[ x = 25 \][/tex]

So, they use 25 cups of flour with 20 tablespoons of honey.

#### 2. How many cups of flour do they use with 13 tablespoons of honey?

We use the same method to solve this:
[tex]\[ \frac{8 \, \text{tbsp honey}}{10 \, \text{cups flour}} = \frac{13 \, \text{tbsp honey}}{x \, \text{cups flour}} \][/tex]

Cross-multiplying to solve for [tex]\( x \)[/tex]:
[tex]\[ 8x = 13 \times 10 \][/tex]
[tex]\[ 8x = 130 \][/tex]
[tex]\[ x = \frac{130}{8} \][/tex]
[tex]\[ x = 16.25 \][/tex]

So, they use 16.25 cups of flour with 13 tablespoons of honey.

#### 3. How many tablespoons of honey do they use with 20 cups of flour?

For this, we set up the proportion:
[tex]\[ \frac{8 \, \text{tbsp honey}}{10 \, \text{cups flour}} = \frac{x \, \text{tbsp honey}}{20 \, \text{cups flour}} \][/tex]

Cross-multiplying to solve for [tex]\( x \)[/tex]:
[tex]\[ 10x = 8 \times 20 \][/tex]
[tex]\[ 10x = 160 \][/tex]
[tex]\[ x = \frac{160}{10} \][/tex]
[tex]\[ x = 16 \][/tex]

So, they use 16 tablespoons of honey with 20 cups of flour.

### Final Table:

[tex]\[
\begin{array}{|l|l|}
\hline
\text{honey (tbsp)} & \text{flour (c)} \\
\hline
8 & 10 \\
\hline
20 & 25 \\
\hline
13 & 16.25 \\
\hline
16 & 20 \\
\hline
\end{array}
\][/tex]

This table summarizes our calculations for the different quantities of honey and flour used.

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Rewritten by : Barada