Write inequalities to represent the situations below. $$ \begin{array}{l} ext { To qualify for the championship, a runner must complete the race in no more than } \ ext { 50 minutes. } \ ext { Use to represent the time (in minutes) of a runner who qualifies for the championship. } \ ext { To get the } 10 \% ext { discount, a shopper must spend at least \$100. } \ ext { Use } d ext { to represent the spending (in dollars) of a shopper who gets the discount. } \ \square\end{array} $$

Question

Write inequalities to represent the situations below. $$ \begin{array}{l}	ext { To qualify for the championship, a runner must complete the race in no more than } \ 	ext { 50 minutes. } \ 	ext { Use to represent the time (in minutes) of a runner who qualifies for the championship. } \ 	ext { To get the } 10 \% 	ext { discount, a shopper must spend at least \$100. } \ 	ext { Use } d 	ext { to represent the spending (in dollars) of a shopper who gets the discount. } \ \square\end{array} $$

UpStudy AI · Accepted Answer

Certainly! Let's define the variables and write the corresponding inequalities for each situation.

### 1. Qualification for the Championship

- **Variable Definition:**  
  Let $$ t $$ represent the time (in minutes) of a runner.

- **Inequality Statement:**  
  To qualify for the championship, a runner must complete the race in **no more than** 50 minutes. This can be expressed as:
  $$
  t \leq 50
  $$

- **Explanation:**  
    The symbol $$ \leq $$ means "less than or equal to." So, any runner who completes the race in 50 minutes or less ($$ t \leq 50 $$) qualifies for the championship.

### 2. Eligibility for the 10% Discount

- **Variable Definition:**  
  Let $$ d $$ represent the spending (in dollars) of a shopper.

- **Inequality Statement:**  
  To receive a 10% discount, a shopper must spend **at least** \$100. This can be expressed as:
  $$
  d \geq 100
  $$

- **Explanation:**  
    The symbol $$ \geq $$ means "greater than or equal to." Therefore, any shopper who spends \$100 or more ($$ d \geq 100 $$) is eligible for the 10% discount.

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**Summary of Inequalities:**
1. **Runner's Time:** $$ t \leq 50 $$
2. **Shopper's Spending:** $$ d \geq 100 $$

These inequalities effectively represent the conditions required for qualifying for the championship and obtaining the discount.
To qualify for the championship, a runner must complete the race in no more than 50 minutes, so $$ t \leq 50 $$. To get a 10% discount, a shopper must spend at least \$100, so $$ d \geq 100 $$.

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