Question

Question 1
A cooking club offers two ways to buy gourmet spice jars. Members pay a one-time fee of $ 48 to join and then $6.75 per spice jar. Non-members pay $9 per spice jar with no membership fee.


Part 1: Which equation represents when the total cost is the same for members and non-members after buying j, the number of jars?

Responses

48 + 6.75j = 9j
48 + 6.75j = 9j EndFragment

48 + 9j = 6.75j
48 + 9j = 6.75j EndFragment

48 = 9j - 6.75j
48 = 9j - 6.75j EndFragment

6.75j = 9j
6.75j = 9j EndFragment
Question 2

Part 2: Complete the sentence below by choosing the correct number of spice jars that best fits the scenario.
(Hint: Round your final answer to the nearest whole number of jars.)


The total cost for members will be less than the cost for non-members after purchasing
Choose...
spice jars.

Answer 1

**Question 1:**

To find the equation that represents when the total cost is the same for members and non-members after buying \( j \) jars, we need to compare the total costs:

- Cost for members: \( 48 + 6.75j \)
- Cost for non-members: \( 9j \)

The costs are equal when:

\[ 48 + 6.75j = 9j \]

So, the correct equation is:

**48 + 6.75j = 9j**

---

**Question 2:**

Now, let's solve the equation \( 48 + 6.75j = 9j \) to find out after how many jars the costs become equal.

1. Start with the equation:
\[ 48 + 6.75j = 9j \]

2. Subtract \( 6.75j \) from both sides:
\[ 48 = 9j - 6.75j \]
\[ 48 = 2.25j \]

3. Now, solve for \( j \):
\[ j = \frac{48}{2.25} \]
\[ j = 21.33 \]

Since we need to round to the nearest whole number, we get:

**j = 21**

So, the total cost for members will be less than the cost for non-members after purchasing:

**21 spice jars.**