Question

If the value of x satisfies the equation \(\frac{{125 \times 4 - x \times 2}}{{x + 50}} = \frac{{200}}{x}\), then the sum of all the possible values of x is?
1. 150
2. 200
3. 100
4. 250

Answer 1

Correct Answer - Option 1 : 150

Given: 

[ ( 125 × 4 ) - ( x × 2 ) ] / ( x + 50 ) = ( 200 / x )

Calculation:

[ ( 125 × 4 ) - ( x × 2 ) ] / ( x + 50 ) = ( 200 / x )

[ 500 - 2x ] / ( x + 50 ) = ( 200 / x ) 

500x - 2x² = 200x + 10000        ∵ cross- multiplication

2x² + 200x - 500x + 10000 = 0 

2x² - 300x + 10000 = 0

x² - 150x + 5000 = 0

To find the roots, we use quadratic formula:

x = { [ ( -b ) ± √ ( b² - 4ac ) ] / 2a }

where a = 1, b = -150, c = 5000

x = { [ ( -(-150 ) ± √ ( (-150)² - 4 × 1 × 5000 ) ] / 2 × 1 }

x = { [ 150 ± 50] / 2 } 

x = 100 or 50 

100 and 50 are the possible values for x. 

Some of the possible values of x are: 100 + 50  = 150 

∴ The sum of the possible values of x is 150.