To find possible combinations of water bottles and shoes that Jaden can purchase, we can set up an inequality system based on the given constraints:
Let x be the number of water bottles and y be the number of pairs of socks (shoes).
1. The total cost should not exceed $2000:
4x + 10y ≤ 2000
2. He needs to buy at least 350 items in total:
x + y ≥ 350
Now, let's look at the possible combinations of x and y that satisfy these constraints:
We'll start with the constraint x + y ≥ 350:
- If x = 0, then y ≥ 350. This means he can buy at least 350 pairs of socks without any water bottles.
- If y = 0, then x ≥ 350. This means he can buy at least 350 water bottles without any pairs of socks.
Now, let's consider the cost constraint 4x + 10y ≤ 2000:
- If he buys only water bottles (y = 0), then the cost is 4x, and 4x should be less than or equal to 2000.
- When x = 0, cost = 4 * 0 = 0 (satisfies the constraint).
- When x = 500 (maximum allowed), cost = 4 * 500 = 2000 (satisfies the constraint).
- If he buys only pairs of socks (x = 0), then the cost is 10y, and 10y should be less than or equal to 2000.
- When y = 0, cost = 10 * 0 = 0 (satisfies the constraint).
- When y = 200 (maximum allowed), cost = 10 * 200 = 2000 (satisfies the constraint).
So, the possible combinations are:
1. Buy at least 350 pairs of socks (y ≥ 350) without any water bottles (x = 0).
2. Buy at least 350 water bottles (x ≥ 350) without any pairs of socks (y = 0).
3. Buy 500 water bottles (x = 500) without any pairs of socks (y = 0).
4. Buy 200 pairs of socks (y = 200) without any water bottles (x = 0).
These are the possible combinations that meet the given constraints.
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