# Linear relations – Comparing Rental Options

The first hall charges a fixed cost of \$1200 plus \$35 per student.

The second hall charges \$1000 plus \$40 per student.

Under which conditions is it better to book the first hall?

The second hall?

### Comments for Linear relations – Comparing Rental Options

 Jul 08, 2013 Linear relations by: Staff Answer First Hall: equation to represent the total cost x = total cost of renting the First Hall n = number of students x = 1200 + 35n Second Hall: equation to represent the total cost y = total cost of renting the Second Hall n = number of students y = 1000 + 40n Break Even Point: the total cost of renting either hall will be the same for a specific number of students x = y 1200 + 35n = 1000 + 40n 1200 + 35n – 35n = 1000 + 40n – 35n 1200 + 0 = 1000 + 5n 1200 = 1000 + 5n 1200 - 1000 = 1000 – 1000 + 5n 200 = 0 + 5n 200 = 5n 5n = 200 5n / 5 = 200 / 5 n = 40 When renting the Hall for 40 students, the cost of renting either hall will be the same: First Hall: x = 1200 + 35n x = 1200 + 35 * 40 x = 2600 Second Hall: y = 1000 + 40n y = 1000 + 40 * 40 y = 2600 When renting for more than 40 students, the cost of the first hall is less expensive. When renting for less than 40 students, the cost of the second hall is less expensive. Thanks for writing. Staff www.solving-math-problems.com