Suppose a video store charges nonmembers $4 to rent each video. A store membership costs $21 and members pay only $2.50 to rent each video. How many videos would one need to rent to justify purchasing a membership?
Let x = number of videos
21 + 2.5x ≤ 4x
Solve for x.
14=X
To determine how many videos one would need to rent to justify purchasing a membership, we can compare the costs of renting videos as a nonmember versus as a member.
As a nonmember, the cost per rental is $4 per video.
As a member, the cost per rental is $2.50 per video, but there is also the initial cost of purchasing a membership, which is $21.
To find the breakeven point, we can set up an equation:
N * $4 = M * $2.50 + $21
where N represents the number of videos rented as a nonmember, and M represents the number of videos rented as a member.
Simplifying the equation:
$4N = $2.50M + $21
To solve for the breakeven point, we need to find the values of N and M where the equation is true. This can be done by substituting different values for N and M until we find a combination that satisfies the equation.
Let's calculate the cost for renting videos for different values of N and M:
For N = 1 and M = 9:
$4 * 1 = $2.50 * 9 + $21
$4 = $22.50 + $21
$4 = $43.50 (This is not true)
For N = 2 and M = 8:
$4 * 2 = $2.50 * 8 + $21
$8 = $20 + $21
$8 = $41 (This is not true)
For N = 3 and M = 7:
$4 * 3 = $2.50 * 7 + $21
$12 = $17.50 + $21
$12 = $38.50 (This is not true)
For N = 4 and M = 6:
$4 * 4 = $2.50 * 6 + $21
$16 = $15 + $21
$16 = $36 (This is not true)
For N = 5 and M = 5:
$4 * 5 = $2.50 * 5 + $21
$20 = $12.50 + $21
$20 = $33.50 (This is not true)
For N = 6 and M = 4:
$4 * 6 = $2.50 * 4 + $21
$24 = $10 + $21
$24 = $31 (This is not true)
For N = 7 and M = 3:
$4 * 7 = $2.50 * 3 + $21
$28 = $7.50 + $21
$28 = $28.50 (This is not true)
For N = 8 and M = 2:
$4 * 8 = $2.50 * 2 + $21
$32 = $5 + $21
$32 = $26 (This is not true)
For N = 9 and M = 1:
$4 * 9 = $2.50 * 1 + $21
$36 = $2.50 + $21
$36 = $23.50 (This is not true)
Based on this analysis, it seems that there is no integer value of N and M that will satisfy the equation and give an equal cost for renting videos as a nonmember and as a member. Therefore, in this case, there is no specific number of videos one needs to rent to justify purchasing a membership. It depends on individual preferences and how often the person plans to rent videos.