To determine the correct statement, we need to analyze the total cost for both members and nonmembers at each quantity of ink cartridges purchased to see if the relationship is proportional.
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Members:
- 0 cartridges: $30
- 1 cartridge: $40
- 2 cartridges: $50
- 3 cartridges: $60
The total cost increases as follows:
- From 0 to 1 cartridge: $40 - $30 = $10
- From 1 to 2 cartridges: $50 - $40 = $10
- From 2 to 3 cartridges: $60 - $50 = $10
The increase is consistent ($10 per cartridge), but to check for proportionality from the origin (0,30), we also calculate the costs as ratios on an adjusted basis:
Total cost for members starting with the $30 membership fee can be expressed as: \( \text{Total Cost} = 30 + 10n \) where n is the number of cartridges purchased. Therefore, it’s not a straight line through (0,0) but it can be linear in terms of additional purchases.
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Nonmembers:
- 0 cartridges: $0
- 1 cartridge: $25
- 2 cartridges: $50
- 3 cartridges: $75
The total cost increases as follows:
- From 0 to 1 cartridge: $25 - $0 = $25
- From 1 to 2 cartridges: $50 - $25 = $25
- From 2 to 3 cartridges: $75 - $50 = $25
The increase is consistent ($25 per cartridge) and when plotted, starts at (0,0) making the relationship proportional.
Given these observations, we conclude that:
- The members do not have a proportional relationship because they start with a $30 base fee; the total cost does not pass through (0,0).
- The nonmembers have a proportional relationship since their costs start from (0,0).
With this analysis, the correct statement is: 1. The relationship between the number of cartridges purchased and the total cost is proportional for nonmembers but not for members.
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