Thread: 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

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

...

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 , and the 2nd debt as , and the 3rd debt as , then you set up a system of equations:


and
then chose a variable, I like , and solve a variable in terms of it and the other one:

Then substitute:




Then begin solving for the other variables using the fact that . You can do that right?

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??

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????

"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