Solving the equation with the variable on both sides

Question

X/2,000 = [X– .11(798)]/1,620
X= 462 

 

The answer is 462. But, I do not understand the process of solving for X that led to the answer. I need a breakdown to understand how the equation is resolved.

 

Thanks!

Answer 1

X/2,000 = [X– .11(798)]/1,620

 

the first thing you want to do is get rid of those fractions by finding the least common multiple of 2000 and 1620. That number is 162,000.

 

[X/2,000] 162,000 = { [X– .11(798)]/1,620} 162,000

 

81x = 100[x - .11(798)]        next simplify the right side by first multiplying  the .11 and 798

                                

81x = 100(x - 87.78)        then using the distributive property to get rid of the 100

81x = 100x - 8778          

 now move the 100x to the other side so that the variable is on one side and the constant is on the other

  81x = 100x - 8778

-100x  -100x

 -19x = -8778        divide both sides by -19

 /-19    /-19

   x = 462

 

Have a great day!

 

 

 

 

Answer 2

So, Peter, we have to find the common denominator. Let's break 2000 and 1620 into their prime factors...

 

2000 = 2⁴(5³)

 

1620 = 2²(3⁴)(5)

 

The common denominator is going to be the highest exponent of every base involved between the two.

 

2⁴(3⁴)(5³)

 

Alright, what is missing from 2000 in that? 3⁴, so we are going to multiply...

 

(x/2000)(81/81) = 81x/162,000

 

What's missing from 1620 in our common denominator? 2²(5²), so we are going to multiply...

 

(x - 87.78)(1620)(100/100) = (100x - 8778)/162,000

 

Believe it or not, now that we have the same denominator, it can go away!

 

81x = 100x - 8778

-19x = -8778

x = 462

 

Boom.