Question

If you pay a one-time fee of $30, you canbuy tickets for a music concert at areduced price of $17. Regular tickets cost$25. Write an inequality that can be usedto determine the number of reduced priceconcert tickets you would need topurchase in order for the total cost to beless expensive than the same number ofregular tickets

Answer 1

When you pay the one-time fee the cost per ticket bought can be expressed by the function below:

$c_1(x)=30+17\cdot x$

While the cost if you don't pay the one-time fee:

$c_2(x)=25\cdot x$

The inequality that can be used to determine the number of tickets you need to buy for the one-time fee to be less expensive is:

$\begin{gathered} c_1(x)Solving the inequality we have:[tex]\begin{gathered} 30<25x-17x \\ 30<8x \\ 8x>30 \\ x>\frac{30}{8} \\ x>3.75 \end{gathered}$

For the "one-time fee" to cost less you need to buy more than 3.75 tickets.