To determine when the two companies will reach a certain price, you have to find out how the companies get their prices in the first place.
For company A, you can see that there is a 20 dollar difference between the cost of a 1,200 ft^2. yard and a 2,000 ft^2. yard, therefore the 800 ft^2 difference costs 20 dollars, which means a single square foot costs 20/800, or .025 or 2.5 cents. Looking at the smallest yard, where 300 sq ft. costs 7.50 and 2.5 * 300 = 750 cents, so the cost of their yards only depends on the size, and there is no surcharge. Price_A in cents = 2.5x where x is square feet.
For company B, there is a 3 dollar difference between 900 and 1,100 square feet, 3/200 = .015, or 1.5 cents per square foot. The 400 size yard costs 16 dollars, where an increase of 400 feet (400*1.5 = 600 cents) should cost 6 dollars, so Company B charges a base price of 10 dollars in addition to the price per square foot. Price_B in cents = 1.5x + 1,000 where x is square feet.
To determine at which size (square feet) the prices are the same, set the companies' prices equal to each other!
Price_A = Price_B, or
2.5x = 1.5x + 1000
2.5x - 1.5x = 1.5x + 1000 - 1.5x
x = 1000
The prices for both companies will be the same for a 1,000 sq ft yard, where both Company A and Company B will charge 2,500 cents or 25 dollars.
