Question

College Algebra: Anyone good with word problems? I'm doing 2x2 Linear Systems and I need to solve this problem using two variables and a system of two equations. I can use any method: Substitution or Addition. This is the problem:
"Two-Income Family: Althea has a higher income than Vaughn and their total income is $82,000. If their salaries differ by $16,000, then what is the income of each?"

Answer 1

So let's call Althea's income A.
And let's call Vaughn's income V.
It says their total income is 82000.
Can you translate that into a math equation?

Answer 2

And we are given Althea's income is higher than Vaughn's.
And we know the incomes differ by 16000.
So you should ale be able to come up with a math equation for this.

Answer 3

x+y=82000
x-y=16000

Answer 4

When I think of total, I think of sum or addition.
When I think of differ by, I think of difference or subtraction.
Or dan can just give you the equations...

Answer 5

:>

Answer 6

lmao nice Dan.
Alright, so since it's trying to figure out the income of each of them, why would it be x+y and x-y?

Answer 7

let x be money earned by althea
let y be money earned by vaughn
x+y=82000
x-y=16000

Answer 8

Okay, But what do I add to that equation? How can I solve it if those are the only two numbers the problem gave?

Answer 9

if x-y=16000
then x=16000+y
x+y=82000
16000+y+y=82000

Answer 10

So, (16,000+y)+y=82,000.
Wouldn't that be 16,001y+y=82,000. Then 16,002y=82,000.