Question

Together, Preston and Horatio have 49 video games. Horatio has 11 more games than Preston. How many games does each person have ?

Answer 1

p + h = 49
h = p + 11
p + p + 11 = 49
2p = 38
Preston has 19 games
Horatio has 30

Answer 2

Preston has 19 games and Horatio has 30 games

Explanation:

This problem is solved by a system of equations. First, the variables are defined:

p: Preston video games

h: Horatio video games

It is known that between them they have 49 video games, that is to say that between them they add 49 games. So the first equation is p+h=49.

On the other hand, it is known that Horatio has 11 video games more than Preston. This means that h=p+11

So, now you have the system of equations. To solve it, there are several methods. In this case the substitution is used, which consists on isolate a variable in one of your equations and replacing on the other equation.

In this case, you have an isolated variable: h=p+11. By replacing it in p+h=49, you get: p+p+11=49

Now you have an equation with a variable, which can be solved:

2*p+11=49

2*p=49-11

2*p=38

`p=(38)/(2)`

p=19

This means that Preston has 19 video games.

Now you have to determinate how many video games have Horatio. For that you know that h=p+11, and you knwo the value of p. Simply replacing you get the value of h

h=p+11

h=19+11

h=30

This means that Horatio has 30 video games.