Patricia is deciding if she wants to join the flower club. If she joins the club she will pay a membership fee of $65. Members will be given a discounted rate for a dozen roses at $10 per dozen. Non-members will pay $18 per dozen roses. How many times would Patricia need to order a dozen roses for the membership to be cheaper than a nonmembership? Set up an inequality for this problem and solve. Is it cheaper to be a member? Why or why not?
Let x be the number of times Patricia needs to order a dozen roses.
The cost of ordering a dozen roses as a non-member is 18 * x.
The cost of ordering a dozen roses as a member is 10 * x + 65.
The inequality to set up for the problem is 10 * x + 65 < 18 * x.
Simplifying the inequality, we get 65 < 8 * x.
Dividing both sides of the inequality by 8, we get 8.125 < x.
Therefore, Patricia would need to order roses at least 9 times for the membership to be cheaper than a non-membership.
To determine if it is cheaper to be a member, we can compare the total cost for ordering roses for each option.
For a member, the total cost is 10 * 9 + 65 = $155.
For a non-member, the total cost is 18 * 9 = $162.
Therefore, it is cheaper to be a member as the total cost for ordering roses is lower when Patricia is a member of the flower club.