# simultaneous equation word problems

• Feb 17th 2010, 04:47 PM
simultaneous equation word problems
Hello Haveing problems with understanding word problems.
A person has incurred 3 debts which total \$ 308
The first debt plus 9 times the 2nd debt plus the 3rd debt is \$ 1124.
Then 2 times the first debt plus the sum of the other two debts is \$ 414.

Determine each of the 3 debts??
Having trouble setting this up.
If you can explain fully would help so I can understand it.
I am in college and never liked word problems.
Thanks
• Feb 17th 2010, 05:16 PM
skeeter
Quote:

Hello Haveing problems with understanding word problems.
A person has incurred 3 debts which total \$ 308

x + y + z = 308

The first debt plus 9 times the 2nd debt plus the 3rd debt is \$ 1124.

x + 9y + z = 1124

Then 2 times the first debt plus the sum of the other two debts is \$ 414.

2x + y + z = 414

...
• Feb 17th 2010, 05:22 PM
Dotdash13
Quote:

Hello Haveing problems with understanding word problems.
A person has incurred 3 debts which total \$ 308
The first debt plus 9 times the 2nd debt plus the 3rd debt is \$ 1124.
Then 2 times the first debt plus the sum of the other two debts is \$ 414.

Determine each of the 3 debts??
Having trouble setting this up.
If you can explain fully would help so I can understand it.
I am in college and never liked word problems.
Thanks

If you have the 1st debt as \$\displaystyle x\$, and the 2nd debt as \$\displaystyle y\$, and the 3rd debt as \$\displaystyle z\$, then you set up a system of equations:
\$\displaystyle x+y+z=308\$
\$\displaystyle x+9y+z=1124\$
and \$\displaystyle 2x+y+z=414\$
then chose a variable, I like \$\displaystyle x\$, and solve a variable in terms of it and the other one:
\$\displaystyle y=308-x-z\$
Then substitute:
\$\displaystyle 2x+y+z=414\$
\$\displaystyle 2x+308-x-z+z=414\$
\$\displaystyle x+308=414\$
\$\displaystyle x=106\$
Then begin solving for the other variables using the fact that \$\displaystyle x=106\$. You can do that right?
• Feb 17th 2010, 05:42 PM
Hello
Hi There,
How do you solve for a single variable if you have 2.
I get x=106, but how do you subsititute it when you still have Z and Y in an equation. How do you get to 1 variable??
• Feb 17th 2010, 06:00 PM
Quote:

Hi There,
How do you solve for a single variable if you have 2.
I get x=106, but how do you subsititute it when you still have Z and Y in an equation. How do you get to 1 variable??

Ok well I came up with -100, 106 and 308 which totals 308.
But can I have a -100????
• Feb 17th 2010, 07:56 PM
Wilmer