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
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.
Sure! I can help you with these two questions. Let's break them down step by step.
1. Lauren works for a bookstore and wants to stay within the store's spending limit while taking advantage of a promotion offered by one of the suppliers. The promotion states that any in-stock children's book costs $4, including tax. Lauren has been told she can spend at most $150 on books for the store. We need to determine how many books Lauren can buy and still stay within the store's spending limit.
a.) To represent the situation as an inequality, we need to consider the total amount Lauren will spend on books. Let's assume she can buy "x" number of books. Each book costs $4, so the total amount spent on books is 4x. Since this amount must be less than or equal to $150, the inequality would be: 4x ≤ 150.
For a.) the inequality you suggested, x ≤ 150, is incorrect because it doesn't represent the total amount spent on books. The correct inequality is 4x ≤ 150, where x represents the number of books.
b.) To determine the solution, we need to solve the inequality 4x ≤ 150. Divide both sides of the inequality by 4 to isolate x: x ≤ 37.5. This means Lauren can buy a maximum of 37 books and still stay within the store's spending limit.
c.) To verify the solution, let's substitute the maximum number of books (x = 37) into the inequality: 4(37) = 148, which is less than or equal to $150. Therefore, the solution is verified.
Now, let's move on to the second question.
2. Customers have two options for accessing a pottery studio: a single-use rate of $37.50 per session or a membership plan that costs $285 for unlimited use annually. We need to determine how many uses in a year would make the membership plan the better option.
a.) To represent this situation as an inequality, we need to compare the costs of the two options. Let's assume the number of uses in a year is represented by "x." The cost of the single-use plan would be 37.50x, while the cost of the membership plan is a fixed $285. Therefore, the inequality would be: 37.50x ≤ 285.
b.) To solve the inequality, divide both sides by 37.50 to isolate x: x ≤ 7.6. This means that if a customer plans to use the pottery studio 7 times or fewer in a year, the membership plan is the better option.
c.) The boundary point, x = 7.6, represents 7 uses in a year. However, since you cannot have a fraction of a use, the reasonable solution would be x = 7. Therefore, the boundary point itself, x = 7, is a reasonable solution to the problem.
I hope this helps you understand how to approach these types of problems. If you have any further questions, feel free to ask!