Final answer:
To represent the situation where Joseph and Jasmine earn points per day, we can use the equation 5x = 8x, where 'x' represents the number of days.
Step-by-step explanation:
To represent the situation where Joseph earns 5 points per day and Jasmine earns 8 points per day, we can use an equation. Let's say 'x' represents the number of days it takes for both Joseph and Jasmine to earn the same number of participation points. Joseph's points can be represented as 5x and Jasmine's points can be represented as 8x. Setting these two expressions equal to each other, we get the equation 5x = 8x. To solve for 'x', we can subtract 5x from both sides of the equation to get 0 = 3x. Then, dividing both sides by 3, we find that x = 0. So, it will take 0 days for Joseph and Jasmine to earn the same number of participation points.