Question

please help me and also l will send the pictures

Answer 1

1/2 cup of salt corresponds to 1/4 cup of pepper, 1/8 cup of garlic powder, and 1/8 cup of onion powder.

Batch 1

To find the equivalent measures to 1 cup of salt, we can use the next proportions:

$\frac{\frac{1}{2}\text{ cup of salt}}{1\text{ cup of salt}}=\frac{\frac{1}{4}\text{ cup of pepper}}{x\text{ cup of pepper}}$

Solving for x,

$\begin{gathered} \frac{1}{2}\cdot x=\frac{1}{4}\cdot1 \\ x=\frac{1}{4}\cdot2 \\ x=\frac{1}{2}\text{ cup of pepper} \end{gathered}$$\begin{gathered} \frac{\frac{1}{2}\text{ cup of salt}}{1\text{ cup of salt}}=\frac{\frac{1}{8}\text{ cup of garlic powder}}{x\text{ cup of garlic powder}} \\ \frac{1}{2}\cdot x=\frac{1}{8}\cdot1 \\ x=\frac{1}{8}\cdot2 \\ x=\frac{1}{4}\text{cup of garlic powder} \end{gathered}$

The amount of onion powder is also 1/4 cup

Batch 2

To find the equivalent measures to 1 cup of pepper, we can use the next proportions:

$\begin{gathered} \frac{\frac{1}{4}\text{ cup of pepper}}{1\text{ cup of pepper}}=\frac{\frac{1}{2}\text{ cup of salt}}{x\text{ cup of salt}} \\ \frac{1}{4}\cdot x=\frac{1}{2}\cdot1 \\ x=\frac{1}{2}\cdot4 \\ x=2\text{ cup of salt} \end{gathered}$$\begin{gathered} \frac{\frac{1}{4}\text{ cup of pepper}}{1\text{ cup of pepper}}=\frac{\frac{1}{8}\text{ cup of garlic powder }}{x\text{ cup of garlic powder}} \\ \frac{1}{4}\cdot x=\frac{1}{8}\cdot1 \\ x=\frac{1}{8}\cdot4 \\ x=\frac{1}{2}\text{ cup of garlic powder} \end{gathered}$

The amount of onion powder is also 1/2 cup

Batch 3

To find the equivalent measures to 1 cup of garlic powder, we can use the next proportions:

$\begin{gathered} \frac{\frac{1}{8}\text{ cup of garlic powder}}{1\text{ cup of garlic powder}}=\frac{\frac{1}{2}\text{ cup of salt}}{x\text{ cup of salt}} \\ \frac{1}{8}\cdot x=\frac{1}{2}\cdot1 \\ x=\frac{1}{2}\cdot8 \\ x=4\text{ cup of salt} \end{gathered}$$\begin{gathered} \frac{\frac{1}{8}\text{cup of garlic powder}}{1\text{ cup of garlic powder}}=\frac{\frac{1}{4}\text{ cup of pepper}}{x\text{ cup of pepper}} \\ \frac{1}{8}\cdot x=\frac{1}{4}\cdot1 \\ x=\frac{1}{4}\cdot8 \\ x=2\text{ cup of pepper} \end{gathered}$$\begin{gathered} \frac{\frac{1}{8}\text{cup of garlic powder }}{1\text{ cup of garlic powder}}=\frac{\frac{1}{8}\text{ cup of onion powder}}{x\text{ cup of onion powder}} \\ \frac{1}{8}\cdot x=\frac{1}{8}\cdot1 \\ x=\frac{1}{8}\cdot8 \\ x=1\text{ cup of onion powder} \end{gathered}$

Part B

One half of the 12 cups of the mixture is salt, one fourth is pepper and one eighth is garlic powder and onion powder. That is,

Salt: 12*1/2 = 6

Pepper: 12*1/4 = 3

Garlic powder: 12*1/8 = 3/2

Onion powder: 12*1/8 = 3/2