Math 2 questions

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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

  • Math 2 questions -

    1.
    let the number of books she can buy be x

    x ≤ 150/4
    x ≤ 37.5 books
    but x must be a whole number, so
    x ≤ 37

    check:
    if she buys 37 books, cost = 4(37) = 148, which is within her limit
    if she buys 38 books, cost = 4(38) = 152 , which goes over her limit of 150

    so x ≤ 37

    2.
    single use: cost = 37.50n, where n is the number of uses
    member use: cost = 285

    we want 37.5n ≤ 285
    divide by 37.5
    n ≤ 285/37.5
    n ≤ 7.6
    but we can't have a partial visit, so consider
    n = 7 or n = 8
    Which one?
    Well, with the single use plan,
    7 visits would cost 7(37.5) or $262.50 which is < 285
    8 visits would cost 8(37.5) or $300 which is > 285

    So for 8 or more visits, the membership plan would be best, for 7 or less the single use plan would be better.

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