Soccer game

Question

Alex scored 3 more goals than sam but together they scored less than 9 goals

Answer 1

(x and y to follow algebra class conventions but...)

Alex + Sam < 9

Alex - Sam = 3

 

We're working with whole numbers (goals) 0 or higher. Answerwould be any 2 numbers totaling 8 or less that are still 3 away from each other. Lowest Sam could get is 0, which puts Alex at 3. Still fits the case Alex + Sam < 9? Yes. Lowest possible total for Alex + Sam is 3+0=3. 

So...formula is:

 

3 <= x+y < 9

 

 

 

 

 

Answer 2

Perfect! So what's the question?

 

I'm assuming you want to figure out how many goals each of them scored, but you're going to have an inequality.

 

Let A be the number of goals Alex scored, S be the number of goals Sam scored.

 

We know that A = S + 3.

We also know that A + S < 9

 

If you make a substitution into the inequality, you would get that (S + 3) + S < 9.

 

Solving that, you have 2S < 6, or S < 3

 

So Sam scored less than 3 goals (or really finitely, 0, 1, or 2 goals). Which also means that Alex scored either 3, 4, or 5 goals.