Question

Molly has 6 grandchildren. She likes to be fair and buy gifts for all of them at the same time. She found jigsaw puzzles, each discounted by 50¢. Find the original cost of each puzzle if she spent a total of $27.(1 point)
Each puzzle cost $.______

Answer 1

Ethan had 7 of his friends over. He ordered cheese pizzas and mozzarella sticks for the 8 of them. In all, there were 64 pieces of food. If each person had 5 slices of pizza, find the number of mozzarella sticks each person ate.(1 point)
Each person ate _____ mozzarella sticks.

Answer 2

Kayla’s mom is planning her birthday party. She has a budget of $150. She knows that the food will cost $5 per person. Twelve friends are coming to the party. Which expression represents the amount of money, m, Kayla’s mom has to spend on each guest’s goody bag?(1 point)
Responses

m+12(5)=150
m plus 12 Left Parenthesis 5 Right Parenthesis equals 150

12m+5=150
12 m plus 5 equals 150

5(m+12)=150
5 Left Parenthesis m plus 12 Right Parenthesis equals 150

12(m+5)=150

Answer 3

Given the equation 8(n+6)=104 , identify the real-world problem that corresponds to this equation.(1 point)

Answer 4

Solve −2(4−n)=24(1 point)
Responses

−8
negative 8

16
16

8
8

−16

Answer 5

One-quarter of the difference of a number and 3 is 2. Find the number.(1 point)
Responses

3 1/2
3 and 1 half

20
20

11
11

5/4

Answer 6

Let the original cost of each puzzle be \( x \).

Since Molly has 6 grandchildren, the total cost for all 6 puzzles at the original price would be \( 6x \).

However, she found the puzzles each discounted by 50¢, which means the discounted price for each puzzle is \( x - 0.50 \).

The total amount she spent on the puzzles is given as $27. Therefore, we can write the equation:

\[
6(x - 0.50) = 27
\]

Now, let's simplify and solve for \( x \):

1. Distribute the 6:
\[
6x - 3 = 27
\]

2. Add 3 to both sides:
\[
6x = 30
\]

3. Divide by 6:
\[
x = 5
\]

Thus, the original cost of each puzzle is \(\$5.00\).

So, each puzzle cost **$5.00**.

Answer 7

Let the total number of people, including Ethan, be 8 (Ethan + 7 friends).

Each person had 5 slices of pizza, so the total number of slices of pizza consumed by all 8 people is:

\[
8 \text{ people} \times 5 \text{ slices/person} = 40 \text{ slices of pizza}
\]

Now, since there are a total of 64 pieces of food (which consists of cheese pizzas and mozzarella sticks), we can find the number of mozzarella sticks by subtracting the number of pizza slices from the total food pieces:

\[
\text{Total pieces of food} - \text{Total slices of pizza} = \text{Total mozzarella sticks}
\]

\[
64 - 40 = 24 \text{ mozzarella sticks}
\]

Next, we need to find out how many mozzarella sticks each person ate. Since there are 8 people, we can divide the total number of mozzarella sticks by the number of people:

\[
\frac{24 \text{ mozzarella sticks}}{8 \text{ people}} = 3 \text{ mozzarella sticks/person}
\]

Thus, each person ate **3 mozzarella sticks**.

Answer 8

To find the correct expression representing the amount of money, \( m \), that Kayla’s mom has to spend on each guest’s goody bag, we can break down the budget into the amount spent on food and the amount spent on goody bags.

1. **Cost of food for 12 friends**: Since food costs $5 per person, for 12 people, the total cost of food will be:
\[
12 \times 5 = 60
\]

2. **Remaining budget for goody bags**: The total budget is $150. After spending $60 on food, the remaining budget for goody bags is:
\[
150 - 60 = 90
\]

Let \( m \) represent the amount of money spent on each guest's goody bag. Since there are 12 guests, the total cost for goody bags can be expressed as:
\[
12m
\]

Since the total cost for food and goody bags must equal the budget, we can set up the equation:
\[
12m + 60 = 150
\]

To find the amount of money available for each guest's goody bag, we rearrange the equation:
\[
12m = 150 - 60
\]
\[
12m = 90
\]

The expression that represents the total cost of goody bags along with the cost of food set to equal the budget can be simplified to the following choice from the options provided:

**12(m + 5) = 150**

This represents the total budget equaling the total spent on food and goody bags, making **12(m + 5)** the best expression to represent the situation.

So, the correct expression is:
\[
12(m + 5) = 150
\]

Answer 9

The equation \( 8(n + 6) = 104 \) can represent a real-world problem involving a group of people combining a fixed amount of something and additional contributions. Here’s a possible scenario:

**Problem:**

Imagine a class of 8 students who are organizing a group project, and they need to buy supplies for it. Each student is responsible for contributing the same amount, but they also need to add a shared fixed cost, such as a project kit containing some basic supplies that costs $6.

The total cost for the entire project, including both the individual contributions and the shared cost, is $104. In the equation, \( n \) represents the amount each student contributes beyond the shared cost.

So, when you multiply the total contribution per student \( (n + 6) \) by the number of students (8), it equals the total budget of $104.

### In summary:
**Real-World Problem Statement:**
*A class of 8 students is collecting money to buy supplies for a project. Each student is contributing an equal amount, and there is a fixed shared cost of $6. If the total amount collected is $104, how much is each student contributing beyond the shared cost?*

Answer 10

To solve the equation \(-2(4 - n) = 24\), we will first distribute the \(-2\) on the left side of the equation.

Step 1: Distribute \(-2\):

\[
-2 \cdot 4 + 2n = 24
\]

This simplifies to:

\[
-8 + 2n = 24
\]

Step 2: Add 8 to both sides of the equation:

\[
2n = 24 + 8
\]

This simplifies to:

\[
2n = 32
\]

Step 3: Divide both sides by 2:

\[
n = \frac{32}{2}
\]

This gives:

\[
n = 16
\]

Thus, the solution to the equation is:

**16**.

Answer 11

Let's denote the unknown number as \( x \).

According to the problem, one-quarter of the difference of a number and 3 is equal to 2. This can be translated into the equation:

\[
\frac{1}{4}(x - 3) = 2
\]

Now, we will solve for \( x \).

Step 1: Eliminate the fraction by multiplying both sides of the equation by 4:

\[
x - 3 = 8
\]

Step 2: Add 3 to both sides:

\[
x = 8 + 3
\]

This simplifies to:

\[
x = 11
\]

Therefore, the number is **11**.