To determine which statement is supported by the table, we need to analyze the relationship between the number of ink cartridges purchased and the total cost for both members and nonmembers.
For members:
- When buying 0 cartridges, the cost is $30.
- When buying 1 cartridge, the cost is $40.
- When buying 2 cartridges, the cost is $50.
- When buying 3 cartridges, the cost is $60.
The total cost for members increases by $10 for each additional cartridge purchased after the initial fee of $30. The cost per cartridge for purchases 1, 2, and 3 is:
- 1 cartridge: $40 - $30 = $10
- 2 cartridges: $50 - $30 = $20 (for 2 cartridges, which averages $10 each)
- 3 cartridges: $60 - $30 = $30 (for 3 cartridges, which averages $10 each)
For nonmembers:
- When buying 0 cartridges, the cost is $0.
- When buying 1 cartridge, the cost is $25.
- When buying 2 cartridges, the cost is $50.
- When buying 3 cartridges, the cost is $75.
The total cost for nonmembers increases as follows:
- 1 cartridge: $25
- 2 cartridges: $50 (which averages $25 each)
- 3 cartridges: $75 (which averages $25 each)
Now, let's check for proportional relationships:
- For members, the cost starts at $30 (a fixed fee), and the incremental cost for cartridges does not yield a constant ratio to the original value. Hence, it’s not proportional.
- For nonmembers, the cost when starting from zero is proportional since the cost increases consistently with each additional cartridge purchased starting from 0.
Thus, the correct statement is:
The relationship between the number of cartridges purchased and the total cost is proportional for nonmembers but not for members.
11 answers