how do i solve this word problem?

Question

a video rental club charges $15 for membership and $2.50 per video. another club charges $5 for membership and $3 for each video rented. how many videos must u rent to make the first club more economical? SHOW ALL WORK please

Answer 1

Let us assume that we rent out x videos.
Therefore, for the first video shop, the cost is 15+2.5x.
For the second video shop, the cost is 5+3x.

Let us equate them so that the cost becomes equal.
15+2.5x=5+3x.
.5x=10
x=20
Therefore, you need to rent more than 20 videos from the first shop to make it more economical.

Answer 2

The cost of joining the first club and renting n videos is

15 + 2.5n

the cost per video is then

(15 + 2.5n)/n

the cost of joining the second club and renting n videos is

5 + 3n

and the cost per video is

(5 + 3n)/n

What you want to know is, when will the unit cost for the first become less than the second, as n increases? Ie, as the number of videos you rent increases. So, let the first cost be less than the second:

(15 + 2.5n)/n < (5 + 3n) /n

and solve for an inequality in n. Your answer will be something like n > X.xxxx, and because you can't have a fraction of a video, round up to the nearest whole number.

Answer 3

You are paying $10 extra for membership in the first club (i.e. $15 less $10) while you save 50 cents for every video rented from club one.

Hence, you need to rent in excess of 20 videos (i.e $10 divide by 50 cents) for the first club to me more economical.

Hope this helps

Answer 4

More economical, meaning afordable? 2.50 x 15=37.50

and 5 x 3=15

1st club: 15/2.50= 6 videos
2nd club: 5/3=1.6=2 , so most likely the 1st club

Answer 5

At 21 days, the club with the $15.00 membership fee becomes more economical. After renting videos for 21 days the $15.00 club cost goes to $67.50, while the $5.00 club cost rises to $68.00.

Answer 6

let x be the minimum number of videos you have to rent to make the first club more economical

$15+$2.5x<$5+$3x
$10<$0.5x
20 x>20

so you have to rent at least 21 videos to make the first club more economical...

Answer 7

15 + 2.5m = 5 + 3m
10 + 2.5m = 3m
10 = .5m
20 = m
m = 20

This sets them to equal. to make it economically correct you would have to rent one more video with the first, so 21 movies would have to be rented.

Answer 8

15+2.5*x<5+3x
-0.5x<-10
0.5x>10
x>20

Answer 9

15+2.5x=y
5+3x=y
15+2.5x=5+3x
10=.5x
x=20

Answer 10

all I can say is ask a genius