Question

1. mp problem solving a group of friends go scuba diving. they rent a boat for x days and scuba gear for y people, represented by the equation 250x + 50y = 1000.

a. graph the equation and interpret the inter
b. how many friends can go scuba diving if they rent the boat for 1 day? 2 days?
c. how much money is spent in total?

1. mp modeling real life

Explanation:

Part b:

Step1: Set \( x = 1 \) (1 day boat rental)

We have the equation \( 250x + 50y = 1000 \). Substitute \( x = 1 \):
\( 250(1) + 50y = 1000 \)
\( 250 + 50y = 1000 \)

Step2: Solve for \( y \)

Subtract 250 from both sides:
\( 50y = 1000 - 250 \)
\( 50y = 750 \)

Divide both sides by 50:
\( y = \frac{750}{50} = 15 \)

Step3: Set \( x = 2 \) (2 days boat rental)

Substitute \( x = 2 \) into \( 250x + 50y = 1000 \):
\( 250(2) + 50y = 1000 \)
\( 500 + 50y = 1000 \)

Step4: Solve for \( y \)

Subtract 500 from both sides:
\( 50y = 1000 - 500 \)
\( 50y = 500 \)

Divide by 50:
\( y = \frac{500}{50} = 10 \)

Part c:

Step1: Assume \( x = 1 \) (1 day) and \( y = 15 \) (from part b)

Total cost = Boat cost + Gear cost
Boat cost: \( 250x = 250(1) = 250 \)
Gear cost: \( 50y = 50(15) = 750 \)

Step2: Calculate total

Total = \( 250 + 750 = 1000 \) (matches the equation, as expected).

(If \( x = 2 \), \( y = 10 \)):
Boat cost: \( 250(2) = 500 \)
Gear cost: \( 50(10) = 500 \)
Total = \( 500 + 500 = 1000 \).

Answer:

s:

Part b:

• 1 day boat rental: \( \boldsymbol{15} \) friends.
• 2 days boat rental: \( \boldsymbol{10} \) friends.

Part c:

Total money spent: \( \boldsymbol{1000} \) (for either 1 day/15 friends or 2 days/10 friends, as the equation is \( 250x + 50y = 1000 \)).