SOLUTION: Can someone help with the below: On Jan 1, a video store sold over 100 video rental memberships. A customer has 4 membership options to choose from: Option 1: 1 month membershi

Question 1139866: Can someone help with the below:
On Jan 1, a video store sold over 100 video rental memberships. A customer has 4 membership options to choose from:
Option 1: 1 month membership for $21.25
Option 2: 3 month membership for $59.95
Option 3: 6 month membership for $94.50
Option 4: 12 month membership for $159.99

The gym made $722.50 from Option 1 memberships and $839.30 from Option 2. They sold 3 times as many Option 3 memberships as Option 4 and made $864.57 more from Option 3 than Option 4
How many memberships did the video rental sell on Jan 1?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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