Final answer:
The equation that will solve for the number of credits Josan and Adamas must earn to have the same amount of play time is 6 + 10 + 5z = 10 + 10z. However, there is no solution for this equation. Josan and Adamas cannot have the same play time.
Step-by-step explanation:
To determine the number of credits, z, that Josan and Adamas must earn to have the same amount of play time, we need to set up an equation.
Let's represent Josan's total play time in minutes as x. Since Josan starts each day with 6 free credits and has already used 10 minutes, Josan's play time can be expressed as x = 6 + 10 + 5z, where z is the number of credits Josan needs to earn.
Similarly, Adamas's total play time in minutes can be represented as y, and it can be expressed as y = 10 + 10z, where z is the number of credits Adamas needs to earn.
Since we want Josan and Adamas to have the same play time, we can set up the equation x = y:
6 + 10 + 5z = 10 + 10z
To solve for z, we can subtract 6 from both sides and subtract 10z from both sides:
5z - 10z = 10 - 6
Simplifying, we get -5z = 4.
Dividing both sides by -5, we find that z = -4/5.
However, since we cannot have a negative number of credits, we can conclude that there is no solution. Josan and Adamas cannot have the same play time.