Final answer:
The value of x is approximately 14.29 percent, which is obtained by setting up an equation for increasing 60 by x percent and decreasing 80 by x percent, and then solving for x.
Step-by-step explanation:
To find the value of x when increasing 60 by x percent gives the same result as decreasing 80 by x percent, we'll set up an equation. Increasing 60 by x percent means we multiply 60 by (1 + x/100), and decreasing 80 by x percent means multiplying 80 by (1 - x/100). Therefore, we'll have the following equation:
60 × (1 + x/100) = 80 × (1 - x/100)
To solve for x, we would first expand both sides:
60 + 0.6x = 80 - 0.8x
Now, combine like terms and solve for x:
0.6x + 0.8x = 80 - 60
1.4x = 20
x = 20 / 1.4
x = 14.2857...
So, the value of x is approximately 14.29 percent. This means that increasing 60 by approximately 14.29 percent will give the same result as decreasing 80 by approximately 14.29 percent.