Final answer:
Katte can purchase 5 plants and 5 bags of soil for $70, 6 plants and 6 bags of soil for $84, or 7 plants and 7 bags of soil for $98 to stay within her $100 budget.
Step-by-step explanation:
Katte is planning her garden purchases with a budget constraint. Given that she wants to buy at least 5 plants at a cost of $10 each and at least one bag of soil for each plant at $4 per bag, and her spending limit is $100, we need to find combinations of plants and bags of soil that fit within this budget.
To start, we know buying 5 plants (the minimum) would cost 5 x $10 = $50. For each plant, we need at least one bag of soil, which would be an additional 5 x $4 = $20, bringing us to a total of $70. This leaves us $30 for additional plants or bags of soil.
- Combination 1: 5 plants and 5 bags of soil for $70
- Combination 2: 6 plants and 6 bags of soil for $10 x 6 + $4 x 6 = $84
- Combination 3: 7 plants and 7 bags of soil for $10 x 7 + $4 x 7 = $98
These three combinations allow Katte to stay within her budget of $100 while meeting her criteria for a minimum number of plants and soil bags.