Question

Martin wants to join a book club to get discount books. Store A charges a joining fee of $75 plus $10 per book. Store B does not have a joining fee and charges $15 per book. What is the greatest number of books Martin can buy so that the total cost at Store A is less than the total cost at Store B?

Answer 1

To find the greatest number of books Martin can buy so that the total cost at Store A is less than the total cost at Store B, we can set up inequalities to compare the costs at each store. By solving these inequalities, we find that Martin can buy a maximum of 15 books.

Step-by-step explanation:

To find the greatest number of books Martin can buy so that the total cost at Store A is less than the total cost at Store B, we need to compare the costs at each store.

1. Let's assume Martin wants to buy 'x' books.
2. At Store A, the total cost is given by the equation 'Cost at Store A = joining fee + (cost per book * number of books)'. So, the cost at Store A is $75 + ($10 * x).
3. At Store B, the total cost is given by the equation 'Cost at Store B = cost per book * number of books'. So, the cost at Store B is $15 * x.
4. We want to find the value of 'x' for which the cost at Store A is less than the cost at Store B. So, we set up the inequality '75 + 10x < 15x'. Solving this inequality, we get '75 < 5x', which simplifies to 'x > 15'.

Therefore, Martin can buy a maximum of 15 books so that the total cost at Store A is less than the total cost at Store B.

Answer 2

Step-by-step explanation:

cost at store A :

cost(b) = 10b + 75

cost at store B :

cosr(b) = 15b

b = the number of books bought.

to answer the question find for what b both functions deliver the same result :

10b + 75 = 15b

75 = 5b

b = 15

when buying the 15th book both costs are the same.

to keep the costs of store A truly less than the costs of store B the limit is therefore 14 books.