Algebra question

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labmonk

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Aug 27, 2010
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I've forgotten how to solve this, and I hope I'm in the right board, but I've forgotten even what catagory problem this is. Thanks
a/b = .227507
(a-1)/b = .223524
 
Thanks for the quick reply. I'm not a student, it's a real life thing I'm trying to solve rather than learn how to solve, but since what I have is a hint, i'll give it a shot. Beware, the last algebra I did was about 35 years ago.

since b = .227507/a, maybe i can just substitute that in equation 1 and get

a/(.227507/a) = .227507 which i think is the same as
a/1 * a/.227507 = .227507
2a/.227507 = .227507
2a= .227507 * .227507
2a = .051759
a = .0258795
b= .1137525

no no, that can't be right
 
Denis said:
b = .227507/a
Click to expand...

I think Denis meant to type b = a/.227507

Starting with the given equation a/b = 0.227507:

Divide both sides by 0.227507

Multiply both sides by b

These two steps solve for b in terms of a.

Now, substitute this result for b into the second equation.

 
I'm in worse trouble since I thought Denis's original was correct:
a/b = .22750
divide both sides by a
(a/b)/a = .227507/a
a/b * 1/a = .227507/a
a's cancel out on the left leaving b=.227507/a?
Can someone end my misery please.
 
b=a/.227507 substituted into the second equation:

(a-1)/(a/.227507) = .223524
(a-1) * .227507/a = .223524
(a-1) * 227507 / (a-1) *a = .223524
.227507/a = .223524
a = .223524/.227507
a = .9825

I think I messed up somewhere
 
labmonk said:
a's cancel out on the left leaving b = .227507/a Based on your subsequent post, I'm thinking that this is a typographical error.

b = a/0.227507
Click to expand...

I'm looking at your subsequent work …



MY EDIT: Fixed oversight

 
labmonk said:
b = a/.227507 substituted into the second equation:

(a-1)/(a/.227507) = .223524
(a-1) * .227507/a = .223524
(a-1) * 227507 / (a-1) *a = .223524 ? Don't do this. Multiply both sides by a, instead.
Click to expand...

After multiplying both sides by a, you should have:

(a - 1)(0.227507) = a(0.223524)

 
labmonk said:
I'm confused, which is it?
Click to expand...

Egads, we're all goofing up on this exercise.

I was looking at your subsequent post, in which you typed the correct ratio for b. I didn't realize that you changed it from one post to the next.

This is correct:

b = a/0.227507

Sorry for any confusion.

 
b=a/.227507 substituted into the second equation:

(a-1)/(a/.227507) = .223524
(a-1) * .227507/a = .223524
multiply both sides by a, instead
(a-1) * .227507 = .223524 * a
I don't remember what to do with (a-1)
 
Yikes...very sorry, I goofed:
a/b = .227507 : b = .227507 / a
(a-1)/b = .223524 : b = .223524/(a-1)
Should be:
a/b = .227507 : b = a /.227507 [1]
(a-1)/b = .223524 : b = (a-1)/.223524 [2]
SO (since [1]=[2]):

a /.227507 = (a-1)/.223524
.223524a = .227507(a-1)
.223524a = .227507a - .227507
.227507a - .223524a = .227507
.003963a = .227507
a = .227507 / .003963 = 57.1195...

and (since b = a /.227507 [1]):
b= 57.1195 /.227507 = 251.067...
 
labmonk said:
(a-1) * .227507 = .223524 * a

I don't remember what to do with (a-1)

Use the Distributive Property.

0.227507 * (a - 1) = 0.227507 * a - 0.227507 * 1
Click to expand...
 
labmonk said:
a/b = .227507
(a-1)/b = .223524
Click to expand...
I find doing it this way is a bit easier:

let x = .227507 and y = .223524

So we have:
a/b = x ; b = a/x [1]
(a-1) / b = y ; b = (a-1)/y [2]

[1][2]:
a/x = (a-1)/y
ay = x(a-1)
ay = ax - x
ax - ay = x
a(x - y) = x
a = x / (x - y) ; now substitute back in...
 
labmonk said:
I'm not a student, it's a real life thing I'm trying to solve rather than learn how to solve
Click to expand...

I regret that I missed this statement, too. :(

If I had seen it earlier, I would have simply posted the solution.

("When it rains, it pours")

 
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