The sum of 2 numbers is 400.If the first number is decreased by 20% and the second number is decreased by 15% then the sum would be 68 less than 400.Find the numbers after the decreasing.
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wht is the answer
To find the numbers after the decreasing, let's assume the two numbers are x and y.
According to the problem, the sum of the two numbers is 400, so we have the equation:
x + y = 400 ...(Equation 1)
We are also given that when the first number is decreased by 20% and the second number is decreased by 15%, the sum is 68 less than 400. Let's calculate the new values of the numbers:
First number after decreasing: x - (20% of x) = x - 0.2x = 0.8x
Second number after decreasing: y - (15% of y) = y - 0.15y = 0.85y
The sum of the decreased numbers is given as 68 less than 400:
0.8x + 0.85y = 400 - 68
0.8x + 0.85y = 332 ...(Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system to find the values of x and y.
Subtracting Equation 1 from Equation 2:
(0.8x + 0.85y) - (x + y) = 332 - 400
0.8x + 0.85y - x - y = -68
Rearranging terms:
-0.2x - 0.15y = -68
Multiplying through by -1 to simplify:
0.2x + 0.15y = 68 ...(Equation 3)
Now we have a system of two equations (Equation 1 and Equation 3). We can solve this system to find the values of x and y.
Solving Equation 1 and Equation 3 simultaneously will give us the values of x and y.
x+y = 400
.80x + .85y = 400-68
...