Math Snap

STEP 1

Assumptions1. The tract was sold for $,200 per acre. The total area of the tract is40 acres3. The profit was14.5\% of the sale price4. We need to find the original cost of the tract

STEP 2

First, we need to find the total sale price of the tract. We can do this by multiplying the sale price per acre by the total number of acres.
$$Sale\, price = Price\, per\, acre \\times Total\, acres$$

STEP 3

Now, plug in the given values for the price per acre and total acres to calculate the sale price.
Sale\, price = \($\)2,200 \\times40

STEP 4

Calculate the total sale price.
Sale\, price = \($\)2,200 \\times40 = \($\)88,000

STEP 5

Now that we have the sale price, we can find the profit. The profit is14.5\% of the sale price.
$$Profit = Sale\, price \\times Profit\, rate$$

STEP 6

Convert the profit rate from a percentage to a decimal.
$$14.5\% =0.145$$$$Profit = Sale\, price \\times0.145$$

STEP 7

Plug in the values for the sale price and the profit rate to calculate the profit.
Profit = \($\)88,000 \\times0.145

STEP 8

Calculate the profit.
Profit = \($\)88,000 \\times0.145 = \($\)12,760

STEP 9

Now that we have the profit, we can find the original cost of the tract. The original cost is the sale price minus the profit.
$$Original\, cost = Sale\, price - Profit$$

STEP 10

Plug in the values for the sale price and the profit to calculate the original cost.
Original\, cost = \($\)88,000 - \($\)12,760

Calculate the original cost.
Original\, cost = \($\)88,000 - \($\),760 = \($\)75,240The original cost of the tract was $75,240.