You are starting a new landscaping business. You have fixed startup costs of 5,600 and monthly variable costs of 200 per week. Your expected income is 900 per week. How many weeks will it take to break even? Answer Attemptiout of 3 (A) Additional Solution ()No Solution square weeks

To find the break-even point, we need to determine the number of weeks it takes for the total income to equal the total costs.<br /><br />Let's denote the number of weeks as \( w \).<br /><br />The total costs can be calculated as the sum of the fixed startup costs and the monthly variable costs multiplied by the number of weeks:<br />\[ \text{Total costs} = \$5,600 + (\$200 \times w) \]<br /><br />The total income can be calculated as the expected income multiplied by the number of weeks:<br />\[ \text{Total income} = \$900 \times w \]<br /><br />To find the break-even point, we set the total income equal to the total costs and solve for \( w \):<br />\[ \$900 \times w = \$5,600 + \$200 \times w \]<br /><br />Now, let's solve this equation step by step:<br /><br />1. Subtract \( \$200 \times w \) from both sides of the equation:<br />\[ \$900 \times w - \$200 \times w = \$5,600 \]<br />\[ \$700 \times w = \$5,600 \]<br /><br />2. Divide both sides of the equation by \( \$700 \):<br />\[ w = \frac{\$5,600}{\$700} \]<br />\[ w = 8 \]<br /><br />Therefore, it will take 8 weeks to break even.