Question

Children under 10 years and older people over 65 years receive a discount on movie tickets. Let x represent the age of a person who receives a discount.

Which inequality represents the age of a child who receives a discount?
?????????


Which inequality represents the age of an older person who receives a discount? x > 65

Which compound inequality represents the age of a person who receives a discount?
?????????

for **Inequality for a child receiving a discount:** \( x < 10 \) its not that

same with **Compound inequality for a person receiving a discount:** \( x < 10 \quad \text{or} \quad x > 65 \) not that either

Answer 1

its Which inequality represents the age of a child who receives a discount?


0 < x < 10

Which inequality represents the age of an older person who receives a discount?


x > 65

Which compound inequality represents the age of a person who receives a discount?


0 < x < 10 or x > 65



Layla deposits at least 25% but no more than 50% of her paycheck into a savings account. If she earns $200 per paycheck, which statements about the amount of money she deposits, s, are true? Check all that apply.

25 ≤ s ≤ 50
50 ≤ s ≤ 100
s ≤ 25 or s ≥ 50
s ≤ 50 or s ≥ 100
She could deposit $50.
She could deposit $75.

Answer 2

Let's break down the requirements for discounts based on age:

1. **Children under 10 years receive a discount:**
- This means we can represent the age of a child with the inequality \( x < 10 \).

2. **Older people over 65 years receive a discount:**
- This age group is represented by the inequality \( x > 65 \).

3. **The compound inequality that represents a person who receives a discount includes both groups:**
- Since the discounts apply to two distinct age ranges (ages under 10 and over 65), we combine them into a compound statement. The correct representation is:
\[
x < 10 \quad \text{or} \quad x > 65
\]

So, the answers are:

- **Inequality for a child receiving a discount:** \( x < 10 \)
- **Inequality for an older person receiving a discount:** \( x > 65 \)
- **Compound inequality representing a person who receives a discount:** \( x < 10 \quad \text{or} \quad x > 65 \)

Please let me know if you need further clarification or assistance!

Answer 3

To analyze Layla's deposit situation based on her earnings of $200 and the deposit percentages (25% to 50%), we can calculate the minimum and maximum amounts she can deposit:

1. **Minimum Deposit (25% of $200):**
\[
0.25 \times 200 = 50
\]

2. **Maximum Deposit (50% of $200):**
\[
0.50 \times 200 = 100
\]

So, Layla must deposit at least $50 and at most $100 into her savings account. This means that we can represent her deposits, \( s \), with the inequality:
\[
50 \leq s \leq 100
\]

Now, let's evaluate the statements provided:

1. **25 ≤ s ≤ 50:** *False* (This includes amounts less than $50, which are not allowed.)

2. **50 ≤ s ≤ 100:** *True* (Correct, as per the derived inequality.)

3. **s ≤ 25 or s ≥ 50:** *False* (This includes amounts less than $50, which are not allowed.)

4. **s ≤ 50 or s ≥ 100:** *False* (This incorrectly includes amounts less than $50 and more than $100, which aren't allowed.)

5. **She could deposit $50:** *True* (This is the minimum deposit amount.)

6. **She could deposit $75:** *True* (This is within the range of $50 to $100.)

### Summary of correct answers:
- **50 ≤ s ≤ 100**
- **She could deposit $50.**
- **She could deposit $75.**