# Word Problem Equations

• Feb 20th 2010, 04:41 PM
Annb
Word Problem Equation:1st try
I'm completely lost with this one....

A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P is linear. If 300 units sold results in $4650 profit and 375 units results in$9000 profit write the equation that models the profit.

What I got was 4350x-1300350

using the y-y1=m(x-x1)
(Nerd)
• Feb 20th 2010, 07:27 PM
integral
I got
$\displaystyle y=58x-12750$

(Bow)
• Feb 20th 2010, 07:31 PM
Annb
How did you get that answer? : (
• Feb 20th 2010, 08:06 PM
Wilmer
Quote:

Originally Posted by Annb
A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P is linear. If 300 units sold results in $4650 profit and 375 units results in$9000 profit write the equation that models the profit.
What I got was 4350x-1300350
using the y-y1=m(x-x1)

Huh?
You have 2 points: (300,4650) and (375,9000)

linear equation using 2 points - Google Search=
• Feb 20th 2010, 08:13 PM
integral
$\displaystyle y=ax+b$
$\displaystyle y_i=ax_i+b$

$\displaystyle y=4650$
$\displaystyle x=300$
$\displaystyle y_i=9000$
$\displaystyle x_i=375$

subtract both equations, cancel B out
$\displaystyle y-y_i=a(x-x_i)$

$\displaystyle -4350=-75a$
$\displaystyle a=\frac{-4350}{-75}=58$

place a in an orig. equation
$\displaystyle y=ax+b$
$\displaystyle 4650=58(300)+b=17400+b$
$\displaystyle 4650-17400=b$
$\displaystyle b=-12750$

plug in

$\displaystyle y=58x-12750$
• Feb 21st 2010, 02:03 AM
jgv115
Most simple way:

$\displaystyle \frac{y-y_{1}}{x-x_{1}} = \frac {y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute values in to get

$\displaystyle 75y-348750=4350x-1631250$

Divide 75 to get

$\displaystyle y-4650=58x-21750$

$\displaystyle y+17100=58x$

$\displaystyle y=58x-17100$ In the form of $\displaystyle y=mx+c$

My answer is different to integrals's but this is just to let you know you can use the 2 point formula.
• Feb 21st 2010, 02:12 AM
HallsofIvy
Quote:

Originally Posted by jgv115
Most simple way:

$\displaystyle \frac{y-y_{1}}{x-x_{1}} = \frac {y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute values in to get

$\displaystyle 75y-348750=4350x-1631250$

Divide 75 to get

$\displaystyle y+8550-19x$

You've lost a "="!
• Feb 21st 2010, 02:32 AM
jgv115
corrected =]