I have a questions that states the following:


Some friends bought a sailboat together and shared the cost equally. If two fewer friends had been involved, each of the others would have paid $3000 more. If one more friend had been involved each of the others would have paid $1000 less.

How many people owned a share of the sailboat?

I think that the equation goes x-2 = y + 3000 for one situation and x+1 = y-1000.

My problem is how do I solve with two unknown variables?

Could somebody please help me understand how to do this and if possible provide me a final answer so that when I solve the problem on my own will have the right answer to compare.

Thanks

For 2 unknown variables with 2 equations, you can solve by elimination or substitution.

Elimination is a bit more powerful, but substitution is easier to explain, so I'll show you substitution.

I'll leave you to work out what the equations are from the question and apply it to your own problem, I'll show you how to solve it with a similar problem.

Say you have 2 equations:

x+5 = y-2
x+19 = 2y

then to solve by substitution, you take one of the equations and rearrange it so that you have a definition of one of your variables. In this case I'll take the first equation and work out an expression for x in terms of y.

x+5 = y-2 --> x = y-7

Now, we substitute this definition into the second equation for x

x+19 = 2y --> y-7+19 = 2y

We can now solve this equation for y, as there is only one unknown.

y = 12

We can now put this value into either of the top 2 equations to find:

x = 5

We can check these values with the other equation, too.

Elimination is similar, but involves subtracting one equation from the other (which has been multiplied up) in order to eliminate a variable.

I hope this helps. Let me know if you have further questions.