Question 1139866
let x = the number of option 3 memberships.
let y = the number of option 4 memberships.


you are given that the number of option 3 memberships is 3 times the number of option 4 memberships.


you are also given that option 3 memberships made 864.57 more than option 4 memberships in total.


each option 3 membership costs 94.50
each option 4 membership costs 159.99


this leads to the following equations.


94.50 * x = 159.99 * y + 864.57
x = 3 * y


the first equation tells you that the total money made from option 3 memberships is equal to the total money made from option 4 memberships plus 864.57.


the second equation tells you that the number of option 3 memberships is equal to 3 times the number of option 4 memberships.


replace x in the first equation by 3 *  from the second equation to get:


94.50 * 3 * y = 159.99 * y + 864.57


simplify to get 283.5 * y = 159.99 * y + 864.57


subtract 159.99 * y from both sides of the equation to get:


283.5 * y - 159.99 * y = 864.57


combine like terms to get:


123.51 * y = 864.57


solve for y to get y = 864.57 / 123.51 = 7


since x = 3 * y, then x = 21.


you have:


x = 21 and y = 7.


21 * 94.50 = 1984.5
7 * 159.99 = 1119.93


1984.5 - 1119.93 = 864.57


that says that the total amount of money earned from option 3 memberships is 864.57 more than the total amount of money earned from option 4 memberships.


this confirms the solution is correct.


you were asked:


How many memberships did the video rental sell on Jan 1?


722.50 from option 1 memberships divided by 21.25 each = 34 option 1 memberships.


839.50 from option 2 memberships divided by 59.95 each = 14 option 2 memberships.


there were 21 option 3 memberships and 7 option 4 memberships.


the total number of option 1 to 4 memberships was 34 + 14 + 21 + 7 = 76 memberships.


that's not more than 100 but that's what it works out to be and i don't see how it could be anything else based on the information that was provided.