Gray bought two plots of land for a total of 120000 on the first plot she made a profit of 15% on the second plot she lost 10% .her total profit 5500, how much did she pay for each piece of land? (Please show the whole procedure of this math with the rough works) Thank you so much !!
To solve this problem, let's assume the cost of the first plot of land as x, and the cost of the second plot as y.
Given information:
1. The total cost of both plots is $120,000.
So, x + y = 120000 ----(1)
2. Gray made a profit of 15% on the first plot.
This means that the selling price of the first plot is (x + 0.15x) = 1.15x.
And the profit she made on the first plot is (0.15x).
3. Gray made a loss of 10% on the second plot.
This means that the selling price of the second plot is (y - 0.10y) = 0.90y.
And the loss she made on the second plot is (0.10y).
4. Her total profit is $5500.
So, the equation will be: (0.15x - 0.10y) = 5500 ----(2)
Now, let's solve these equations to find the values of x and y.
From equation (1), we can rewrite it as:
x = 120000 - y ----(3)
Substituting the value of x from equation (3) into equation (2), we get:
(0.15*(120000 - y) - 0.10y) = 5500
Simplifying the equation:
18000 - 0.15y - 0.10y = 5500
0.25y = 18000 - 5500
0.25y = 12500
y = 12500 / 0.25
y = 50000
Now, substitute the value of y into equation (1) to find the value of x:
x = 120000 - 50000
x = 70000
Therefore, Gray paid $70,000 for the first plot of land and $50,000 for the second plot of land.