# Thread: How to solve a word problem with 3 variables

1. ## How to solve a word problem with 3 variables

Here is the question. Sal, Martin, and Gloria are partners in a welding business. Because of the differences in their contributions, it is decided that Golria's share of the profits will be one-and-a-half times as much as Sal's share, and that Martin's share will be twice as much as Gloria's share. How should a profit of $48,200.00 be divided? If I could only find out what Sal's portion is then I know that would be multiplied by 1.5 and that would give me Goloria's portion which I would multiply by 2 which would give me Martin's portion then add Sal plus Gloria plus Martin should equal$48,200.00. However the most important variable I need to solve for I don't know how to set up the equation. If someone would be as kind as to break this down step by step showing me what to write in algebra form I would really appreciate it. Thanks again.

2. Let x = Sal's share
Let 1.5x = Gloria's share
Let 2(1.5x) = 3x = Martin's share

Now x + 1.5x + 3x = $48,200 implies 5.5x =$48, 200
implies x = $8763.64 So, Sal earns$8763,64, Gloria earns 1.5(8763.64)=$13145.45 and Martin earns$26,290.91

3. ## how to solve a word problem

Thankyou GoldendoodleMom I was really confused. But you made it look so simple and easy. I've spend a couple of days on this one I really wanted to get it. Was one of my mistakes assigning each person a different letter variable I was using X=Sal, Y=Goloria and Z=Martin.
So Y=1.5X and Z=2y then I really got confused trying to move thing around it was a mess. How come I tried setting up the equation this way?

4. Let's say we just look at Sal's share.

We call Sal's share $s$.

We are told that Gloria will get 1.5 times as much as Sal. Simply put, this is 1.5 times Sal's share, s, which is 1.5s.

We are then told that Martin gets 2 times what Gloria gets. Which means that this is 2 times Gloria's share, which is 1.5s. This is 2 x 1.5 s = 3s.

So, now we have it all in one variable.

You could put it in 3 variables, but ultimately, you would have to know how the three variables relate to one another to solve the problem.