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 made 10% profit her total profit 5500, how much did she pay for each piece of land? (And please show the full procedure of the math even the rough work as well,Thank you so much!)
Please show the full procedure of this math solution even with the rough works? thank you
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i understood 15 percent will b add with 10 percent then multiply with (120000-x) ....and what is that x after that 15 ...i am so confused
Let's assume Gray paid x dollars for the first plot of land and y dollars for the second plot of land.
According to the given information, the total cost of both plots is $120,000:
x + y = 120,000 ---(Equation 1)
Now, let's calculate the profit on each plot:
Profit on the first plot = 15% of x = 0.15x
Profit on the second plot = 10% of y = 0.10y
We are also given that the total profit on both plots is $5,500:
0.15x + 0.10y = 5,500 ---(Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we need to solve simultaneously to find the values of x and y.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method in this case.
Multiply Equation 1 by 0.10 and Equation 2 by 100 to eliminate the decimals:
0.10x + 0.10y = 12,000 ---(Equation 3)
15x + 10y = 550,000 ---(Equation 4)
Now subtract Equation 3 from Equation 4:
(15x + 10y) - (0.10x + 0.10y) = 550,000 - 12,000
14.9x + 9.9y = 538,000
Simplify and rearrange the equation:
14.9x = 538,000 - 9.9y
x = (538,000 - 9.9y) / 14.9 ---(Equation 5)
Now substitute the value of x from Equation 5 into Equation 1:
(538,000 - 9.9y) / 14.9 + y = 120,000
Multiply through by 14.9 to get rid of the denominator:
538,000 - 9.9y + 14.9y = 1,788,000
Combine like terms:
5y = 1,250,000
Divide both sides by 5:
y = 250,000
Now substitute the value of y back into Equation 1 to solve for x:
x + 250,000 = 120,000
Subtract 250,000 from both sides:
x = -130,000
Since we can't have a negative price for land, we know that something went wrong in our calculations or assumptions. Please double-check the given information to ensure its accuracy.
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