To represent the context of Jai's points system, we can set up an equation based on the points he receives for signing up and the points he earns for each visit.
Jai starts with 20 points from signing up, and for each visit he makes (which we'll denote as \( x \)), he earns an additional 11.5 points. To find out how many visits he needs to make to earn at least 181 points, we can formulate the equation as follows:
\[ 20 + 11.5x = 181 \]
In this equation:
- \( 20 \) represents the initial points earned from signing up.
- \( 11.5x \) represents the points earned from visits (where \( x \) is the number of visits).
- \( 181 \) is the total points needed for a free movie ticket.
Thus, the number of visits \( x \) can be solved from this equation to find out how many visits Jai needs to make to get a free movie ticket.
Alternatively, a tape diagram could illustrate the relationship by showing:
- A segment representing the fixed 20 initial points.
- Several segments each representing 11.5 points for each visit Jai makes, summing to the total of 181 points.
Both representations convey similar information, but the equation is a direct mathematical representation of the situation.