200k views
3 votes
Jaden has no more than $2000 to purchase water bottles and pairs of socks for a fundraiser for his school’s cross-country team. Water bottles cost $4 and shoes cost $10. He needs to buy a total of at least 350 items without buying too many of just one item. Which of the following are possible combinations of water bottles and shoes he can purchase?

1 Answer

6 votes
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.

tangina ok
User Homayoun Behzadian
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories