# Thread: Help me figure out equations.

1. ## Help me figure out equations.

The only thing I need help with is figuring out these equations. :[

Your grandfather has $303,000 to invest. He has decided to invest all of it by purchasing some shares of stock in each of three companies: a lumber company that sells for$25 per share and has an expected growth of 6.5% per year, a fast food company that sells for $30 per share and has an expected growth of 10% per year and a discount clothing chain that sells for$15 per share and has an expected growth of 12% per year. The total cost of the lumber company shares exceeds the total cost of the clothing chain by $15,000. If the total growth of all the tree is$28,425 for the year, how many shares of each did he buy?

My equations are...

Let -
x = lumber / 25 / 6.5%
y = food / 30 / 10%
z = clothing / 15 / 12%

25x+30y+15z = 303,000
.065x+.1y+.12z = 28,425
-x+z = 15,000

Where did I go wrong? Any help would be greatly appreciated.

2. .065x+.1y+.12z = 28,425
This equation is wrong.
x, y and z are the number of shares. To find the annual profit, you have to multiply the cost of each share to x, y and z.
So
0.065*25x+ 0.1*30y+ 0.12*15z = 28,425

3. Hello, Yep!

Your grandfather has $303,000 to invest. He has decided to invest all of it by purchasing some shares of stock in three companies: a lumber company that sells for$25 per share and has an expected growth of 6.5% per year,
a fast food company that sells for $30 per share and has an expected growth of 10% per year, a discount clothing chain that sells for$15 per share and has an expected growth of 12% per year.
The total cost of the lumber company shares exceeds the total cost of the clothing chain by $15,000. If the total growth of all three is$28,425 for the year, how many shares of each did he buy?

Let -
x = lumber / 25 / 6.5%
y = food / 30 / 10%
z = clothing / 15 / 12%

My equations are:

. . $25x+30y+15z \:=\: 303,000$
. . $0.065x+0.1y+0.12z \:=\: 28,425$
. . $-x+z \:=\: 15,000$ . ← Here!

Where did I go wrong?

Lumber is 15,000 more than Clothing: . $x \:=\:z + 15,000 \quad\Rightarrow\quad x - z \:=\:15,000$