I'll retype it, Ive been waiting forever and i just need someone to do these 2 questions so that i can continue doing my other ones so can someone do them: I need help with 2 questions so that I could do my other ones myself so can someone please do these 2 questions so i get an example how to do them, thanks.
1. Lauren works for a bookstore. One of the stores suppliers has a promotion in which any in stock childrens book cost $4 incliding tax/ Laurn has been told that she can spend at most $150 on books for the store. How many books can lauren buy and stay within the store's spending limit.
a.) Use an inequality to represent the situation.
b.) Determine the solution and use it to solve the problem.
c.) verify your solution
For a.) i got x < or equal to 150, is it right?
2. Customers can use a pottery studio's kiln and equipment. They can pay in 2 ways for access to the studio. How many uses in a year would make the mebers plan the better option?
studio access rates:
single use: $37.50 per session
Members plan: $285 for unlimited use annually
a.) use an inequality to represent the situation
b.) use the ineqaulity to solve the problem
c.)is the boudary point itself a reasonable solution to the problem?
YES, NO ,EXPLAIN
done, see your previous post of this
For the first question:
a) To represent the situation using an inequality, let's assume the number of children's books Lauren can buy is x. Since each book costs $4, including tax, the total amount spent on books can be calculated by multiplying the cost per book ($4) by the number of books (x). The inequality would be:
4x ≤ 150
This inequality represents the condition where the total amount spent on books (4x) should be less than or equal to $150.
b) To determine the solution, we need to solve the inequality. By dividing both sides of the inequality by 4, we get:
x ≤ 37.5
So, Lauren can buy at most 37 children's books within the store's spending limit.
c) To verify the solution, substitute the value of x (37) back into the inequality:
4(37) ≤ 150
148 ≤ 150
Since 148 is less than or equal to 150, the solution is verified as correct.
For the second question:
a) To represent the situation using an inequality, let's assume the number of uses in a year for the membership plan is x. The cost for a single-use is $37.50 per session, so the total cost for single-use access in a year would be 37.50x. The membership plan costs $285 for unlimited use annually. The inequality would be:
37.50x > 285
This inequality represents the condition where the total cost for single-use access should be greater than the cost of the membership plan.
b) To solve the inequality, divide both sides by 37.50:
x > 285/37.50
Simplifying the right side, x > 7.6
So, if the number of uses in a year (x) is greater than 7.6, the membership plan would be the better option.
c) No, the boundary point itself (x = 7.6) is not a reasonable solution to the problem since you cannot have a fraction of a use. In this case, you would either pay for 7 uses or 8 uses. So, the answer would be 8 uses, which is greater than the boundary point.