   SEARCH HOME Math Central Quandaries & Queries  Question from kimberly, a student: at+b=ar-c, solve for a Kimberley,

Let's do it first with specific numbers for t, b, r and c and then see if we can mimic the steps when these variables don't have specific values.

5a + 7 = 3a - 9, solve for a.

I would first add -3a to both sides to get

5a + 7 - 3a = 3a - 9 - 3a

and rearrange to get

5a - 3a + 7 = -9.

Next add -7 to each side and also notice that 5a and -3a have a common factor of a. Thus the equation becomes

(5 - 3)a = -9 -7.

Since I have specific numeric values I can perform he arithmetic to get

2a = -16.

Finally divide both sides by 2 to get the answer

a = -16/2 = -8.

Ok, now back to the original problem.

at + b = ar - c, solve for a.

The first step is to add -ar to both sides.

at + b - ar = ar - c - ar.

Again a rearrangement gives

at - ar + b = -c.

Notice here that at and -ar have a common factor of a.

Complete the solution mimicking the steps above and let me know what you get for a.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.