4th Edition Algebra Chapter 5 pg 123 #11

[dschuetze]

Hi,

I was hoping someone could help me understand how you solve this equation. The book is not clear on how the answer is solved and simplified. I understand everything up to the part where you substitute the expression for S3 into the first equation to solve for S2, but I am not clear on how the book goes through and solves the equation.

Thanks to anyone who can assist.

[tommywallach]

Heyo,

Yeah, it's confusing, but there really is no better way to do it. Let me try to explain it myself:

The question wants s2. So the equation for s2 would be:

s2 = (s3 + s1)/2

We already have s1, so all we need is s3. Let's try to solve for it:

s3 = (s2 + s4)/2

Uh-oh. We don't have s2, so this doesn't work. HOWEVER, if we replace the equation for s2 in the s3 equation, it will solve:

s3 = ((s3+s1)/2) + s4)/2

Multiply both sides by 2:

2s3 = (s3+s1)/2 + s4

Multiply both sides by 2 again:

4s3 = s3 + s1 +2s4

3s3 = s1 + 2s4

Now we can put in the values we originally knew:

3s3 = 15 + 21

s3 = 12

Now we can finally solve:

s2 = (s3 + s1)/2

s2 = 12 + 15/2

s2 = 13.5

Hope that helps!

-t

[dschuetze]

Thank you very much Tommy, your breakdown made it much more clear than how the book outlined it.

-d

[tommywallach]

Yay!