Final answer:
An athlete's total ticket sales are represented by the expression 10x + 5y, where x and y are the numbers of adult and child tickets sold respectively. The inequality to represent their sales goal is 10x + 5y ≥ 350. Graphing the inequality and using given values, it is determined that selling 10 adult tickets and 30 child tickets, totaling $250, does not meet the $350 goal.
Step-by-step explanation:
To represent the total amount of money an athlete makes from ticket sales, we write the expression 10x + 5y, where x is the number of adult tickets sold, and y is the number of child tickets sold.
The inequality to represent the amount an athlete must make is 10x + 5y ≥ 350. This inequality indicates that the total amount from selling adult and child tickets must be at least $350.
Graphing the Inequality
- To graph the inequality, we plot two points representing the intercepts: if x is 0 (no adult tickets sold), then y must be 70 (350/5) to satisfy the inequality. If y is 0 (no child tickets sold), then x must be 35 (350/10) to satisfy the inequality.
- The graph of this inequality will be a shaded region above and to the right of the line formed by the equation 10x + 5y = 350.
Determining the Ticket Sales Outcome
To determine whether an athlete will bring in at least $350 selling 10 adult and 30 child tickets, we plug in the values to the expression to get (10 × 10) + (5 × 30) = 100 + 150 = 250. Since 250 is less than 350, the athlete will not meet the required amount only by selling 10 adult tickets and 30 child tickets.