# Intermediate alegbraic equation help needed

#### hp2992

##### New member
Hi Guys,

I trust you're all well.

I have labelled this as an intermediate equation although to some, this may seem elementary (please forgive my ignorance).

Looking to solve for Y;

Y = 4500/P + 625 + 87.5[(5821.43 - Y)/28.57]

I'm given the solution of;

Y = 1107.69/P + 4542.31

Have spent a good hour or so trying to deduce the steps in between (it's part of example in a textbook with no indication as to how the solution is derived). I want to ensure I understand the steps before moving on.

Are there any kind mathematicians who can assist?

Your time and assistance will be much appreciated,

Thanks,

H.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi Guys,

I trust you're all well.

I have labelled this as an intermediate equation although to some, this may seem elementary (please forgive my ignorance).

Looking to solve for Y;

Y = 4500/P + 625 + 87.5[(5821.43 - Y)/28.57]

I'm given the solution of;

Y = 1107.69/P + 4542.31

Have spent a good hour or so trying to deduce the steps in between (it's part of example in a textbook with no indication as to how the solution is derived). I want to ensure I understand the steps before moving on.

Are there any kind mathematicians who can assist?

Your time and assistance will be much appreciated,

Thanks,

H.
Did the textbook "just" give you an answer - for an example problem?

Can you please post the steps given to you in the textbook for this problem?

Also please indicate exactly where you get lost in their solution.

#### hp2992

##### New member
Hi Subohotosh,

Pretty much... See question 2 in the pic (IS curve equation given in solution... calculated in a previous example):

Got lost between inserting "r" and solving for "Y"... The last 4 lines.

Thanks,

H

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi Subohotosh,

Pretty much... See question 2 in the pic (IS curve equation given in solution... calculated in a previous example):

View attachment 13229

Got lost between inserting "r" and solving for "Y"... The last 4 lines.

Thanks,

H
What do you get:

87.5/28.57 = ??? ..................................(A)

(87.5/28.57) * 5821.43 = ??? ..................................(B)

#### Harry_the_cat

##### Senior Member
Firstly, expand to get rid of the brackets. This will give 2 terms after the 625 (one involves Y, the other doesn't).

Secondly, collect the Ys on the LHS of the equation and add the constants on the RHS.

Thirdly, divide both sides by co-efficient of Y.

#### hp2992

##### New member

Thanks dude. Was making an elementary mistake with rearranging the equation. The decimals are out... But that's due to my rounding.