Taryn is hosting a party at a restaurant. The restaurant is charging her $160 to rent the space and $17 per guest. If Taryn wants to spend less than $585, which inequality could be used to solve for x, the number of guests Taryn can invite?
A.
$17x < $160
B.
$17x - $160 < $585
C.
$17x < $585
D.
$17x + $160 < $585
The correct inequality that could be used to solve for x, the number of guests Taryn can invite, is C. $17x < $585.
To solve for x, the number of guests Taryn can invite, we need to set up an inequality that represents the given situation. Let's break down the information:
- The restaurant is charging Taryn $160 to rent the space.
- The restaurant is also charging $17 per guest.
To find the total cost of the party, we need to add the cost of renting the space ($160) to the cost per guest multiplied by the number of guests (17x). Then, we can set up an inequality to represent the scenario, where the total cost is less than $585.
Since the total cost is the sum of the rental fee and the cost per guest multiplied by the number of guests, the inequality can be set up as follows:
$17x + $160 < $585.
Therefore, the correct inequality to solve for x is option D: $17x + $160 < $585.