SOLUTION: Ref. Question 1043454: Please list the operations you did after you substituted for y. I still don't understand. Sorry.

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Question 1043539: Ref. Question 1043454:
Please list the operations you did after you substituted for y. I still don't understand. Sorry.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This was already done for you, response and solution from TWO tutors.
Same as question $1043447.

What do you not understand in this solution?
If a is added to the difference of 2 quantities, the sum is b, and if the larger is divided by the smaller, the quotient is c. Determine quantities.

system%28a%2Bx-y=b%2Cx%2Fy=c%29 and you want to solve for x and y.

x%2Fy=c
x=cy
-
substitute for x into the "b" equation and first solve for y.
a%2Bcy-y=b
cy-y=b-a
y%28c-1%29=b-a
highlight%28y=%28b-a%29%2F%28c-1%29%29

You have either of two choices to solve for x. You could use now found y and substitute into either equation, or you could take the ratio equation from the description and solve it for y and then substitute into the "b" equation. I will do this second way.

x%2Fy=c
y%2Fx=1%2Fc
y=x%2Fc
-
a%2Bx-y=b
x-y=b-a
x-x%2Fc=b-a--------the substitution for y
x%281-1%2Fc%29=b-a
x%28c%2Fc-1%2Fc%29=b-a
x%28c-1%29%2Fc=b-a
x=%28b-a%29%28c%2F%28c-1%29%29
highlight%28x=c%28b-a%29%2F%28c-1%29%29-----solved for x

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Ref. Question 1043454:
Please list the operations you did after you substituted for y. I still don't understand. Sorry.
You seem to want to use 2 equations to solve for x, in terms of 3 other variables. Why didn't you say so when question 1043447 was submitted? 



Question 1043447: If a is added to the difference of 2 quantities, the sum is b, and if the larger is divided by the smaller, the quotient is c. Determine quantities. 

Let x = larger

Let y = smaller 

My attempt: 

x - y + a = b 

x / y = c 

How do I proceed ? 



Apparently, you want to solve for x using the following equations: 

x - y + a = b______y = x + a - b ------ eq (i)



Since y = x + a - b, and y+=+x%2Fc, it follows that: x+%2B+a+-+b+=+x%2Fc

cx + ac - bc = x ------- Multiplying by LCD, c

x - cx = ac - bc

x(1 - c) = ac - bc