SOLUTION: This equation is not from a textbook, it's directly from my professor. I'm having difficulties trying to remember how to solve for 'x' in the following situation: ($80 + ($1,00

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: This equation is not from a textbook, it's directly from my professor. I'm having difficulties trying to remember how to solve for 'x' in the following situation: ($80 + ($1,00      Log On


   

Question 186822: This equation is not from a textbook, it's directly from my professor. I'm having difficulties trying to remember how to solve for 'x' in the following situation:
($80 + ($1,000 - X) / 12) / (($1,000 + X) / 2) = 0.07
If I divide by the denominator, I end up with Xs on both sides of the equation. Please help! Thank You!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%2880+%2B+%281000+-+x%29+%2F+12%29+%2F+%28%281000+%2B+x%29+%2F+2%29+=+0.07 Start with the given equation.


Take note that the LCD of the inner fractions is 12.


Multiply EVERY term (that's either part of a fraction or by itself) by the LCD 12 to clear the inner fractions.


Note: because we're multiplying every term on the left side by the same number, it's like we're multiplying the left side by 12%2F12 which is simply 1. So the equation has NOT changed.


%2812%2880%29+%2B+1000+-+x%29%2F%286%281000+%2B+x%29%29=0.07 Simplify


%28960+%2B+1000+-+x%29%2F%286%281000+%2B+x%29%29=0.07 Multiply


%281960+-+x%29%2F%286%281000+%2B+x%29%29=0.07 Combine like terms.


%281960+-+x%29%2F%286000+%2B+6x%29=0.07 Distribute


1960+-+x=0.07%286000+%2B+6x%29 Multiply both sides by 6000+%2B+6x.


1960+-+x=0.07%286000%29+%2B+0.07%286x%29 Distribute


1960+-+x=420+%2B+0.42x Multiply


100%281960-x%29=100%28420%2B0.42x%29 Multiply both sides by 100 to clear out the decimals.


196000-100x=42000%2B42x Distribute and multiply.


-100x=42000%2B42x-196000 Subtract 196000 from both sides.


-100x-42x=42000-196000 Subtract 42x from both sides.


-142x=42000-196000 Combine like terms on the left side.


-142x=-154000 Combine like terms on the right side.


x=%28-154000%29%2F%28-142%29 Divide both sides by -142 to isolate x.


x=77000%2F71 Reduce.


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Answer:

So the answer is x=77000%2F71 which approximates to x=1084.507.


Note: since this problem looks like it deals with money, I would go with the approximated solution x=1084.507 and round it to two places to get x=1084.51