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.
### 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.
