To determine the minimum number of tortillas Chloe must sell in order to break even, we need to understand two key terms: Total Cost and Total Income.
1. Total Cost:
This is the sum of the costs for making tortillas and the rent for the stall. The cost to make one tortilla is R5, and the stall rent is R500. The total cost formula can be written as:
[tex]\[ \text{Total Cost} = ( \text{cost per tortilla} \times \text{number of tortillas} ) + \text{stall rent} \][/tex]
[tex]\[ \text{Total Cost} = (5 \times \text{number of tortillas}) + 500 \][/tex]
2. Total Income:
This is the amount of money Chloe earns by selling tortillas. She sells each tortilla for R1. The total income formula can be written as:
[tex]\[ \text{Total Income} = \text{price per tortilla} \times \text{number of tortillas} \][/tex]
[tex]\[ \text{Total Income} = 1 \times \text{number of tortillas} \][/tex]
Break-even Point:
The break-even point is where total income equals total cost. Mathematically, we set the total income equal to the total cost and solve for the number of tortillas:
[tex]\[ \text{Total Income} = \text{Total Cost} \][/tex]
[tex]\[ 1 \times \text{number of tortillas} = 5 \times \text{number of tortillas} + 500 \][/tex]
To isolate the number of tortillas (let's call it [tex]\( n \)[/tex]), you subtract the cost component that's proportional to the number of tortillas from both sides:
[tex]\[ n = 5n + 500 \][/tex]
[tex]\[ n - 5n = 500 \][/tex]
[tex]\[ -4n = 500 \][/tex]
[tex]\[ n = -\frac{500}{-4} \][/tex]
[tex]\[ n = 125 \][/tex]
Therefore, Chloe needs to sell a minimum of 125 tortillas to break even. This means the income from selling 125 tortillas will cover both the cost of making the tortillas and the stall rent.
