High School

14. Sophia bought 9 red peppers for $5.40.

**Part A:** Find the unit rate. Then use the unit rate to write an equation relating the cost in dollars \([tex]c[/tex]\) to the number of red peppers \([tex]p[/tex]\).

**Part B:** How much would Sophia pay for 14 red peppers?

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15. A salad dressing recipe uses 12 parts oil, 3 parts vinegar, and 2 parts honey. Which of the following sets of ingredients are in a proportional relationship with the recipe? Select all that apply.

A. 9 Tbsp oil, 2 Tbsp vinegar, 1.5 Tbsp honey

B. 6 Tbsp oil, 1.5 Tbsp vinegar, 1 Tbsp honey

C. 15 Tbsp oil, 4 Tbsp vinegar, 3 Tbsp honey

D. 18 Tbsp oil, 4.5 Tbsp vinegar, 3 Tbsp honey

E. 24 Tbsp oil, 6 Tbsp vinegar, 4 Tbsp honey

Answer :

Sure, let's solve each part of the question step-by-step:

### Part A: Finding the Unit Rate and Writing the Equation

Step 1: Calculate the unit rate (cost per red pepper).

Sophia bought 9 red peppers for [tex]$5.40. To find the unit rate, we divide the total cost by the number of red peppers:
\[ \text{Unit rate} = \frac{\$[/tex]5.40}{9 \text{ peppers}} = \[tex]$0.60 \text{ per pepper} \]

Step 2: Write the equation relating the cost \( c \) to the number of red peppers \( p \).

Since each red pepper costs $[/tex]0.60:
[tex]\[ c = 0.60p \][/tex]

This equation tells us that the total cost [tex]\( c \)[/tex] in dollars is equal to 0.60 times the number of red peppers [tex]\( p \)[/tex].

### Part B: Calculating the Cost for 14 Red Peppers

Using the unit rate we found and the equation:
[tex]\[ c = 0.60p \][/tex]

If Sophia wants to buy 14 red peppers:
[tex]\[ c = 0.60 \times 14 = \$8.40 \][/tex]

So, Sophia would pay [tex]$8.40 for 14 red peppers.

### Question 15: Checking Proportional Relationships

The original salad dressing recipe uses 12 parts oil, 3 parts vinegar, and 2 parts honey. We need to check which of the following sets of ingredients are in the same proportional relationship.

Step 1: Check each set of ingredients one by one.

1. Set A: 9 Tbsp oil, 2 Tbsp vinegar, 1.5 Tbsp honey
\[ \frac{9}{12} = 0.75, \ \frac{2}{3} ≈ 0.67, \ \frac{1.5}{2} = 0.75 \]
The ratios are not the same, so Set A is not proportional.

2. Set B: 6 Tbsp oil, 1.5 Tbsp vinegar, 1 Tbsp honey
\[ \frac{6}{12} = 0.5, \ \frac{1.5}{3} = 0.5, \ \frac{1}{2} = 0.5 \]
The ratios are the same, so Set B is proportional.

3. Set C: 15 Tbsp oil, 4 Tbsp vinegar, 3 Tbsp honey
\[ \frac{15}{12} = 1.25, \ \frac{4}{3} ≈ 1.33, \ \frac{3}{2} = 1.5 \]
The ratios are not the same, so Set C is not proportional.

4. Set D: 18 Tbsp oil, 4.5 Tbsp vinegar, 3 Tbsp honey
\[ \frac{18}{12} = 1.5, \ \frac{4.5}{3} = 1.5, \ \frac{3}{2} = 1.5 \]
The ratios are the same, so Set D is proportional.

5. Set E: 24 Tbsp oil, 6 Tbsp vinegar, 4 Tbsp honey
\[ \frac{24}{12} = 2, \ \frac{6}{3} = 2, \ \frac{4}{2} = 2 \]
The ratios are the same, so Set E is proportional.

### Summary

- Unit rate: $[/tex]0.60 per red pepper
- Equation: [tex]\( c = 0.60p \)[/tex]
- Cost for 14 red peppers: $8.40
- Proportional sets: Set B, Set D, Set E

These detailed steps should help you understand how to solve this type of problem.