Can someone please check my answer?
Rearrange (cp-yd)/(pd)=p+y to make d the subject
OK, I did
cp-yd=pd(p+y)
cp=pd(p+y)+yd
cp=p^d+pdy+yd
factoring out the d
cp=d(p^2+py+y)
cp/(p^2+py+y)=d
correct! good job
thanks, wasn't sure whether i could simplify that last line or not
To check if your answer is correct, we can substitute your solution back into the original equation and see if it holds true.
The original equation is: (cp - yd)/(pd) = p + y
Using your solution, we have: d = cp/(p^2 + py + y)
Now let's substitute this value back into the original equation:
(cp - yd)/(pd) = p + y
Substituting d = cp/(p^2 + py + y):
(cp - y(cp/(p^2 + py + y)))/(p(cp/(p^2 + py + y))) = p + y
Multiplying both sides of the equation by p(p^2 + py + y):
p(cp - y(cp/(p^2 + py + y))) = p^2(cp/(p^2 + py + y)) + py(p^2 + py + y)
Simplifying:
cp^2 - y(cp) = pcp/(p^2 + py + y) + p^2y + py^2 + py
Combining like terms:
cp^2 - ycp = p^2cp/(p^2 + py + y) + p^2y + py^2 + py
Now, let's simplify further:
Multiply both sides of the equation by (p^2 + py + y):
cp^2(p^2 + py + y) - ycp(p^2 + py + y) = p^2cp + p^2y(p^2 + py + y) + py^2(p^2 + py + y) + pyp(p^2 + py + y)
Expanding:
c(p^4 + 2p^2y + py^2 + p^2y + 2py^2 + y^3) - y(p^2cp + p^2y + pyp^2 + p^2y^2 + py^3 + yp^3 + y^4) = p^2cp + p^4y + p^3y^2 + p^2y^3 + p^2y + py^3 + p^3y^2 + py^4
Simplifying, we get:
c(p^4 + 2p^2y + py^2 + p^2y + 2py^2 + y^3) - y(p^2cp + p^2y + pyp^2 + p^2y^2 + py^3 + yp^3 + y^4) = p^2cp + p^4y + p^3y^2 + p^2y^3 + p^2y + py^3 + p^3y^2 + py^4
Clearly, the left-hand side of the equation is not equal to the right-hand side, which means your solution for d is incorrect.
To rearrange the equation correctly, we need to isolate the term with d on one side of the equation. Here's the correct method:
Given: (cp - yd)/(pd) = p + y
To make d the subject, we can start by multiplying both sides of the equation by pd:
pd(cp - yd)/(pd) = pd(p + y)
Simplifying:
cp - yd = p^2d + pyd
Next, let's isolate the terms with d on one side by subtracting pyd from both sides:
cp - yd - pyd = p^2d + pyd - pyd
Simplifying further:
cp - yd - pyd = p^2d
Now, factor out d from the left-hand side:
cp - (y + py)d = p^2d
Finally, divide both sides of the equation by (cp - y - py):
(cp - (y + py)d)/(cp - y - py) = p^2d/(cp - y - py)
This gives us the solution for d as:
d = (p^2d)/(cp - y - py)
Therefore, the correct rearrangement of the equation to make d the subject is: d = (p^2d)/(cp - y - py)