Question

Which of the following real-world problems can be modeled with the inequality 384+2x<6x

384
+
2
x
<
6
x
?

Marta charges a flat fee of $384 plus $2 per linear foot to decorate tables for a quinceanera. Carla charges $6 per linear foot to do the same. For what number of linear feet, x, will the cost of both decorators be the same?

Shawna has made 384 campaign buttons for the student council election. She plans to make 2 more buttons each hour. Marguerite plans to make 6 campaign buttons per hour. For what number of hours, x, will Shawna have the same amount of campaign buttons as Marguerite?

Super Clean house cleaning company charges $384 to power wash a house plus $2 per linear foot. Power Bright charges $6 per linear foot and no flat fee. For what number of linear feet, x, will the cost of Super Clean be more expensive than Power Bright?

Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym?

Answer 1

Answer: Gym problem (fourth option)

Explanation:

Hi, to answer this question we have to analyze the options given.

For the first option the equation is:

384+2x=6x

Because the problem asks for a solution where both costs are equal.

For the second option the equation is :

384+2x = 6x

Because the problem asks for a solution where both amounts are equal.

For the third option the inequality is:

384+2x>6x

Because the problem asks for a solution where the first cost is more expensive than the second cost.

For the fourth option (gym problem) the inequality is:

384+2x< 6x

Because the problem asks for a solution where the second cost (super gym) is more expensive than the first cost (mega gym).

This option is the correct one.

Feel free to ask for more if needed or if you did not understand something.