Question

A coffee shop, Lot-O-Latte, currently has 287 club members who earn special discounts. For every 18 new customers, five of them will sign up for the club membership.

Part A: Write an equation to represent the situation. Identify the meaning of all variables used.

Part B: What would a decrease in the y-intercept represent?

Part C: Create a second equation for a shop that is just starting to offer club memberships, with a lower proportion of new customers to club memberships made. Does this equation have the same intercept and slope? Explain your reasoning.

Answer 1

I think that the answer of part a) can be the subsequent equation:
\[y = 287 + 5 \times \left[ {\frac{x}{{18}}} \right]\]

Answer 2

where t is the number of the membership of the coffee shop, and x is the number of new customers. Furthermore, with the symbol [x] I have indicated the integer part of x, namely:
[8.4] = 8 for example

Answer 3

oops... where y is the number of the membership of the coffeee shop...

Answer 4

287

Answer 5

yes! I think so!

Answer 6

ok

Answer 7

for part C, we can suppose that for every 12 new customers only 5 of them will sign up for the club. In that case the fraction new customers to club membership is lower than the one in part A

Answer 8

in that case the equation given for part A, will be as below:
\[y = 287 + 5 \times \left[ {\frac{x}{{12}}} \right]\]

Answer 9

and, as we can see, the y-intercept will be unchanged, since the meaning of the y-intercept is the initial number of club members

Answer 10

so what do i put for the equation on C not the explaining part

Answer 11

I'm sorry I was helping another student.
The answer for Part C is:
the y-intercept is the same, since it represents the initial number of the club members, whereas the slope is greater than the one of Part A.

Answer 12

@itsajw