A A family buys 6 tickets to a show. They also each spend on a snack. They spend
a total of for tickets and snacks.
B Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends.
and then adds 6 more ounces for each.
Here are two equations:

Ask by Mejia Ortega. in the United States

Jan 14,2025

Question

A A family buys 6 tickets to a show. They also each spend on a snack. They spend
a total of for tickets and snacks.
B Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends.
and then adds 6 more ounces for each.
Here are two equations:

Ask by Mejia Ortega. in the United States

Jan 14,2025

UpStudy AI · Accepted Answer

Certainly! Let's tackle each of the two problems you've presented step by step.

---

## **Problem A: Family Tickets and Snacks**

### **Given:**
- **6 tickets** are purchased for a show.
- **Each family member** spends **\$3** on a snack.
- **Total expenditure** on tickets and snacks is **\$24**.

### **Objective:**
Determine the **cost per ticket**.

### **Assumptions:**
- The family buys **one ticket per family member**.
- Let’s assume the family has **$$ n $$ members**.

### **Setting Up the Equation:**

1. **Cost of Tickets:**
   - **Number of Tickets:** 6
   - **Cost per Ticket:** Let's denote this as **$$ p $$ dollars**.
   - **Total Cost for Tickets:** $$ 6p $$

2. **Cost of Snacks:**
   - **Snack Cost per Member:** \$3
   - **Total Cost for Snacks:** $$ 3n $$ (since each of the $$ n $$ members spends \$3)

3. **Total Expenditure:**
   $$
   6p + 3n = 24
   $$

### **Determining the Number of Family Members ($$ n $$):**

Since **6 tickets** are purchased and it's typical for one ticket per person, it's logical to assume there are **6 family members**. Thus, $$ n = 6 $$.

### **Solving for $$ p $$:**

Substitute $$ n = 6 $$ into the equation:
$$
6p + 3(6) = 24 \
6p + 18 = 24 \
6p = 24 - 18 \
6p = 6 \
p = \frac{6}{6} \
p = 1
$$

### **Conclusion:**
- **Each ticket costs \$1.**

> **Note:** A ticket price of \$1 seems unusually low for most shows. If there's a possibility that the family does **not** have 6 members, the calculation would differ. For example:
>
> - **If the family has 4 members:**
>   $$
>   6p + 3(4) = 24 \
>   6p + 12 = 24 \
>   6p = 12 \
>   p = 2
> $$
>   - **Each ticket would cost \$2.**
>
> Ensure the number of family members aligns with the context of the problem for accurate results.

---

## **Problem B: Diego's Juice Distribution**

### **Given:**
- **Diego** has **24 ounces** of juice.
- He **pours equal amounts** for each of his **3 friends**.
- Then he **adds 6 more ounces** to each friend's portion.
- **Equation Provided:** $$ 3(x + 6) = 24 $$

### **Objective:**
Determine the **initial amount** $$ x $$ of juice Diego poured for each friend **before** adding the extra 6 ounces.

### **Understanding the Equation:**

The equation $$ 3(x + 6) = 24 $$ represents the total juice distributed after adding the extra 6 ounces to each friend's initial portion.

- **$$ x $$:** Initial ounces poured to each friend.
- **$$ x + 6 $$:** Total ounces each friend receives after adding 6 ounces.
- **3:** Number of friends.

### **Solving the Equation:**

1. **Start with the equation:**
   $$
   3(x + 6) = 24
   $$

2. **Divide both sides by 3 to solve for $$ x + 6 $$:**
   $$
   x + 6 = \frac{24}{3} \
   x + 6 = 8
   $$

3. **Subtract 6 from both sides to solve for $$ x $$:**
   $$
   x = 8 - 6 \
   x = 2
   $$

### **Conclusion:**
- **Initial amount poured to each friend:** **2 ounces**
- **After adding 6 ounces:** $$ 2 + 6 = 8 $$ ounces per friend
- **Total juice distributed:** $$ 3 \times 8 = 24 $$ ounces (which matches the total juice Diego had)

---

If you have any further questions or need additional clarification on either of these problems, feel free to ask!
Each ticket costs \$1.

A A family buys 6 tickets to a show. They also each spend on a snack. They spend
a total of for tickets and snacks.
B Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends.
and then adds 6 more ounces for each.
Here are two equations:

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A A family buys 6 tickets to a show. They also each spend on a snack. They spend a total of for tickets and snacks. B Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends. and then adds 6 more ounces for each. Here are two equations:

Upstudy AI Solution

Answer

Solution

Extra Insights

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Latest Algebra Questions

A A family buys 6 tickets to a show. They also each spend on a snack. They spend
a total of for tickets and snacks.
B Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends.
and then adds 6 more ounces for each.
Here are two equations: