# Thread: simultaneous equation word problems

1. ## 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 $414. Determine each of the 3 debts?? Having trouble setting this up. If you can explain fully would help so I can understand it. I am in college and never liked word problems. Thanks 2. Originally Posted by bradycat Hello Haveing problems with understanding word problems. A person has incurred 3 debts which total$ 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
...

3. Originally Posted by bradycat
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?

4. ## 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??

5. Originally Posted by bradycat
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????

6. "Work smart, not hard", Brady.
Your 3 equations:
x + y + z = 308 [1]
x + 9y + z = 1124 [2]
2x + y + z = 414 [3]

[2]-[1]: 9y - y = 1124 - 308 ; y = 102

[3]-[1]: 2x - x = 414 - 308 ; x = 106

[1]: 106 +102 + z = 308 ; z = 100