Question

inequalities: apply
try this

read the following real-world story problem. fill in blanks with values of your choice according to the specifications. answer the questions as they are asked.

it is a beautiful day, and 12 friends decide to rent some boats to take out on the lake. the friends have [choose an amount of money between $200 and $350] to spend on renting boats. each boat cost [choose an amount of money between $30 and $50] to rent. write and solve an inequality that represents the number of boats the friends could rents based on the amount of money they have.

the friends read the sign advertising the boats and learn that each boat has a [choose a weight between 750 pounds and 900 pounds] weight limit. the friends know that they each weigh on average 150 pounds. write and solve an inequality that represents the number of friends that could fit in each boat. based on this information, what is the minimum number of boats they need to rent?

use the information from the solutions to your inequalities to write a proposal to the friends about how many boats they should rent. be sure to explain all their options for the number of boats they could rent, which option you think is best, and why. write it as a 6th grader

Answer 1

I picked numbers for the blanks:
- They have $300 to spend.
- Each boat costs $40 to rent.
- Each boat has an 800-pound weight limit.
- Each friend weighs on average 150 pounds and there are 12 friends.

1) Inequality for how many boats they can rent with money
Let b = number of boats.
Cost inequality: 40b ≤ 300
Solve: b ≤ 300/40 = 7.5
Since b must be a whole number, they can rent at most 7 boats. So the possible numbers of boats they could afford are 1, 2, 3, 4, 5, 6, or 7.

2) Inequality for how many friends fit in each boat (weight limit)
Let f = number of friends per boat.
Weight inequality: 150f ≤ 800
Solve: f ≤ 800/150 ≈ 5.33
So at most 5 friends can safely fit in one boat.

Minimum number of boats needed for all 12 friends
If each boat can hold at most 5 friends, the minimum number of boats is the smallest whole number n with 5n ≥ 12.
5 × 2 = 10 (not enough), 5 × 3 = 15 (enough).
So they need at least 3 boats.

Proposal to the friends (6th-grader voice)
Hey everyone! We have $300 and each boat costs $40, so we can rent up to 7 boats. Because each boat can only hold 800 pounds and we each weigh about 150 pounds, only 5 people can ride in one boat safely.

That means:
- The fewest boats we need is 3 (3 boats hold up to 15 people, which is enough for our 12 friends).
- We could also rent 4, 5, 6, or 7 boats because we can afford them.

My pick: rent 4 boats. Here’s why:
- 3 boats would work and is the cheapest (3 × $40 = $120), but that’s up to 5 people in one boat and might feel crowded.
- With 4 boats (4 × $40 = $160) we’d have exactly 3 people in each boat (12 ÷ 4 = 3), which is safer and more comfortable.
- 4 boats are still well under our $300 budget, so we save money and have more space.

So I recommend renting 4 boats. If everyone wants to save the most money and doesn’t mind being a little crowded, we could pick 3 instead.