Name Writing Algebraic Expressions 1. Eric worked a total of 35 hours this week. Write an expression that represents how much money Eiric carned this week. Let $$ w $$ represent how much he Eric carns per hour. 3. Julius earns $$ \$ 12.50 $$ per hour. His most current paycheck included earnings for $$ h $$ hours. His check also included a bonus of $$ \$ 300 $$. Write an expression reflecting how much Julius earned on his paycheck. 5. A website charges $$ \$ 20 $$ for a membership. For each membership, $$ \$ 1 $$ is donated to charity. Write an expression that represents how much money the website earned this month if $$ x $$ number of people signed up for a membership. 2. Tara ran a distance of 5.4 mites. It took Tara $$ h $$ hours to complete her run. Write an expression that represent Tara's rate of speed per hour. 4. Squeaky Clean Maid services charges each customer a $$ \$ 50 \mathrm{fee} $$ and $$ \$ 15 $$ dollars for each hour it takes to complete their job. Write an expression showing how much the cleaning service charges for each job. Let $$ h $$ equal the number of hours it takes to complete a job. 6. A rectangle has a length of 8 inches and a width of $$ w $$. Write an expression that represents the perimeter of the rectangle. 8. Molly is $$ \boldsymbol{n} $$ years old. Julie is 2 more than 3 times the age of Molly. Write an expression to represent Julie's age. per hour. Write an expression to represent how much Valerie earns per hour.

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UpStudy AI · Accepted Answer

Sure! Let's go through each problem and write the corresponding algebraic expressions.

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### **1. Eric's Earnings**

**Problem:**  
Eric worked a total of 35 hours this week. Write an expression that represents how much money Eric earned this week. Let $$ w $$ represent how much he earns per hour.

**Expression:**  
$$ \text{Total Earnings} = 35w $$

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### **2. Tara's Rate of Speed**

**Problem:**  
Tara ran a distance of 5.4 meters. It took Tara $$ h $$ hours to complete her run. Write an expression that represents Tara's rate of speed per hour.

**Expression:**  
$$ \text{Rate of Speed} = \frac{5.4}{h} $$  
*(measured in meters per hour)*

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### **3. Julius's Paycheck**

**Problem:**  
Julius earns \$12.50 per hour. His most recent paycheck included earnings for $$ h $$ hours. His check also included a bonus of \$300. Write an expression reflecting how much Julius earned on his paycheck.

**Expression:**  
$$ \text{Total Earnings} = 12.50h + 300 $$

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### **4. Squeaky Clean Maid Services Charge**

**Problem:**  
Squeaky Clean Maid Services charges each customer a \$50 fee and \$15 for each hour it takes to complete their job. Write an expression showing how much the cleaning service charges for each job. Let $$ h $$ equal the number of hours it takes to complete a job.

**Expression:**  
$$ \text{Total Charge} = 50 + 15h $$

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### **5. Website's Monthly Earnings**

**Problem:**  
A website charges \$20 for a membership. For each membership, \$1 is donated to charity. Write an expression that represents how much money the website earned this month if $$ x $$ number of people signed up for a membership.

**Expression:**  
$$ \text{Total Earnings} = 20x - 1x = 19x $$  
*Alternatively:*  
$$ \text{Total Earnings} = 19x $$

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### **6. Perimeter of a Rectangle**

**Problem:**  
A rectangle has a length of 8 inches and a width of $$ w $$. Write an expression that represents the perimeter of the rectangle.

**Expression:**  
$$ \text{Perimeter} = 2(8) + 2w = 16 + 2w $$

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### **8. Julie's Age**

**Problem:**  
Molly is $$ n $$ years old. Julie is 2 more than 3 times the age of Molly. Write an expression to represent Julie's age.

**Expression:**  
$$ \text{Julie's Age} = 3n + 2 $$

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If you have any more questions or need further clarification on any of these expressions, feel free to ask!
Here are the simplified algebraic expressions for each problem: 1. **Eric's Earnings:** $$ 35w $$ 2. **Tara's Rate of Speed:** $$ \frac{5.4}{h} $$ *(meters per hour)* 3. **Julius's Paycheck:** $$ 12.50h + 300 $$ 4. **Squeaky Clean Maid Services Charge:** $$ 50 + 15h $$ 5. **Website's Monthly Earnings:** $$ 19x $$ 6. **Perimeter of a Rectangle:** $$ 16 + 2w $$ 7. **Julie's Age:** $$ 3n + 2 $$ If you need further assistance or have additional questions, feel free to ask!

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