Expert: Scott A Wilson - 3/3/2010

Question
Hi Scott

I'm trying to rework the following equation to get A=. can you help?

X = ((((A+1.99)/1.175)-(((A*15/100)+0.25))-(B+C))

Many thanks
Kevin

Answer
X = ((((A+1.99)/1.175)-(((A*15/100)+0.25))-(B+C))

This is the same as X = (A+1.99)/1.175 - A*0.15 + 0.25 - B - C.

Breaking down the 1st term gives X = A/1.75 + 1.99/1.175 - A*0.15 + 0.25 - B - C.

Note that 1.75 is 7/4, so 1/1.75 is 4/7.
On 1.99/1.175, 1.99 is the same as 199/100 and 1.175 is the same as 47/40,
so 1.99/1.175 comes out to (199/100)(40/47) = 398/235.
For the next term, note that -0.15 = -3/20.
For the last fraction, note that 0.25 = 1/4.

Rewriting it again using this gives X = 4A/7 + 398/235 - 3A/20 + 1/4 - B - C.
Now note that 4A/7 and -3A/20 need to be multiplied by 20/20 and 7/7, respectively.
This gives 80A/140 and -21A/140.
The combined A's are then 80A/140 - 21A/140 = 59A/140.
Taking the constants, 398/225 and 1/4, the 1st *4/4 is 1592/900 and
the 2nd time 225/225 is 225/900.  Adding these together gives 1817/900.
The other parts of the equation, X, -B, and -C, stay the same.

We now have X = 59A/140 + 1817/900 - B - C.
This can quickly be changed into 59A/140 = X - 1817/900 + B + C.
The only thing left to do is to mulitply each term by 140/59.
This gives A = 140(X+B+C)/59 - 12,719/2655.

I just did it quickly with no calculator, so check the multiplication and division.