The sum of two numbers is 400.If the first number is decreased by 20% and the second number is decreased by 15%, than the sum would be 68 less. Find the numbers after the decrease.
Let's assume the first number is x and the second number is y.
We are given two conditions:
1. The sum of the two numbers is 400.
2. If the first number is decreased by 20% and the second number is decreased by 15%, then the sum would be 68 less.
From the first condition, we have:
x + y = 400
Using the second condition, we can calculate the decreased values of x and y:
Decrease in the first number = 20% of x = 0.2x
Decrease in the second number = 15% of y = 0.15y
The sum after the decrease would be:
(x - 0.2x) + (y - 0.15y) = x - 0.2x + y - 0.15y = 0.8x + 0.85y
According to the second condition, this sum would be 68 less than the original sum (x + y):
0.8x + 0.85y = x + y - 68
Now we have a system of equations:
x + y = 400
0.8x + 0.85y = x + y - 68
Simplifying the second equation:
0.8x + 0.85y = x + y - 68
0.8x - x + 0.85y - y = -68
-0.2x - 0.15y = -68
We can solve this system of equations to find the values of x and y.
To find the numbers after the decrease, let's assume the first number is x and the second number is y.
The given information states that the sum of two numbers is 400:
x + y = 400 ---(equation 1)
It is also given that after decreasing the first number by 20% and the second number by 15%, the sum would be 68 less:
0.8x + 0.85y = 400 - 68
0.8x + 0.85y = 332 ---(equation 2)
Now, we have two equations with two variables. We can solve these equations simultaneously.
To begin, let's solve equation 1 for x:
x = 400 - y
Substitute this value of x into equation 2:
0.8(400 - y) + 0.85y = 332
320 - 0.8y + 0.85y = 332
-0.8y + 0.85y = 332 - 320
0.05y = 12
y = 12 / 0.05
y = 240
Now, substitute the value of y back into equation 1 to find x:
x + 240 = 400
x = 400 - 240
x = 160
Therefore, after decreasing the first number by 20% and the second number by 15%, the first number would be 160 and the second number would be 240.
a + b = 400 ... .8 a + .8 b = 320
.8 a + .85 b = 400 - 68 = 332
subtracting equations (to eliminate a) ... .05 b = 12
multiplying by ... .85 / .05 ... .85 b = 204
substitute back to find .8 a