Question

Heather is looking to join a book club. The first club charges a one-time fee of $5 and $7 for every book you buy.  The second club charges a one-time fee of $15 and $5 for every book you buy.a) Write an equation representing the first club's total cost.  y= b) Write an equation representing the first club's total cost.  y=c) How many books will cause the cost to be the same? booksd) What would be the total cost for when they are the same? $

Answer 1

a) y = 5 + 7n

b) y = 15 + 5n

c) 5 books

d) $40

a) Here, we want to write an equation representing the first club's total cost

Let the number of books bought be n

Then, mathematically;

`y\text{ = 5 + 7n}`

b) For the second club's total cost

Let the number of books bought be n

Then mathematically;

`y\text{ = 15 + 5n}`

c) For the cost to be the same, we equate y in both cases so asto find n

Thus, we have;

`\begin{gathered} 15\text{ + 5n = 5 + 7n} \\ \\ 15-5\text{ = 7n-5n} \\ \\ 10\text{ = 2n} \\ \\ n\text{ = }(10)/(2) \\ \\ n\text{ = 5 books} \end{gathered}`

d) Here, we simply substitute n for 5 in any of the equations

We have this as;

`\begin{gathered} 5\text{ + 7n} \\ \\ 5\text{ + 7(5)} \\ 5\text{ + 35 = 40} \end{gathered}`