Word Problem Equations

**Annb** · February 20th 2010, 04:41 PM

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)

**integral** · February 20th 2010, 07:27 PM

I got
$y=58x-12750$

**Annb** · February 20th 2010, 07:31 PM

How did you get that answer? : (

**Wilmer** · February 20th 2010, 08:06 PM

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=

**integral** · February 20th 2010, 08:13 PM

$y=ax+b$
$y_i=ax_i+b$

$<br /> <br /> y=4650<br />$
$x=300$
$y_i=9000$
$x_i=375$

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

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

place a in an orig. equation
$y=ax+b$
$<br /> 4650=58(300)+b=17400+b$
$4650-17400=b$
$b=-12750$

plug in

$y=58x-12750$

**jgv115** · February 21st 2010, 02:03 AM

Most simple way:

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

Substitute values in to get

$75y-348750=4350x-1631250$

Divide 75 to get

$y-4650=58x-21750$

$y+17100=58x$

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

My answer is different to integrals's but this is just to let you know you can use the 2 point formula.

**HallsofIvy** · February 21st 2010, 02:12 AM

Originally Posted by jgv115

Most simple way:

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

Substitute values in to get

$75y-348750=4350x-1631250$

Divide 75 to get

$y+8550-19x$

You've lost a "="!

**jgv115** · February 21st 2010, 02:32 AM

corrected =]

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