Questions: Caitlyn sells her drawings at the county fair. She wants to sell at least 95 drawings and has portraits and landscapes. She sells the portraits for 18 each and the landscapes for 10 each. She needs to sell at least 1260 worth of drawings in order to earn a profit. Write a system of 2 inequalities to model this situation. Use "x" for the number of portraits and "y" for the number of landscapes. First Inequality: Second Inequality: Solve your system of inequalities by graphing.

Caitlyn sells her drawings at the county fair. She wants to sell at least 95 drawings and has portraits and landscapes. She sells the portraits for 18 each and the landscapes for 10 each. She needs to sell at least 1260 worth of drawings in order to earn a profit.

Write a system of 2 inequalities to model this situation. Use "x" for the number of portraits and "y" for the number of landscapes.

First Inequality:

Second Inequality:

Solve your system of inequalities by graphing.

Transcript text: Caitlyn sells her drawings at the county fair. She wants to sell at least 95 drawings and has portraits and landscapes. She sells the portraits for $18 each and the landscapes for $10 each. She needs to sell at least $1260 worth of drawings in order to earn a profit. Write a system of 2 inequalities to model this situation. Use "x" for the number of portraits and "y" for the number of landscapes. First Inequality: Second Inequality: Solve your system of inequalities by graphing.

Solution

Solution Steps

Step 1: Define Variables

Let $ x $ be the number of portraits and $ y $ be the number of landscapes.

Step 2: Formulate the First Inequality

Caitlyn wants to sell at least 95 drawings in total. Therefore, the first inequality is: \[ x + y \geq 95 \]

Step 3: Formulate the Second Inequality

Caitlyn needs to earn at least $1260 from the sales. She sells portraits for $18 each and landscapes for $10 each. Therefore, the second inequality is: \[ 18x + 10y \geq 1260 \]