Question

A scuba diving resort hotel offers divers two plans. Plan A gives 3 nights’ lodging and 4 dives. Plan B gives 5 nights’ lodging and 8 dives. How much does it cost for each night and each dive?

Answer 1

To find the cost per night and cost per dive, set up a system of linear equations using the given information and solve for x and y.

Step-by-step explanation:

To find the cost per night and cost per dive, we can set up a system of linear equations using the given information:

Let x be the cost per night and y be the cost per dive.

Plan A gives 3 nights’ lodging and 4 dives, so the cost for Plan A can be represented as 3x + 4y.

Plan B gives 5 nights’ lodging and 8 dives, so the cost for Plan B can be represented as 5x + 8y.

We can set up the following system of equations:

1. 3x + 4y = Cost of Plan A
2. 5x + 8y = Cost of Plan B

We can then solve this system of equations to find the values of x and y, which represent the cost per night and the cost per dive respectively.

Answer 2

x = 35 and y = 100

Step-by-step explanation:

Let x = dollar cost per dive and y = dollar cost per night.

ATQ,

4x+3y = 440 .....(1)

and

8x + 5y = 780 .....(2)

Multiply equation (1) by 2.

8x+6y = 880......(3)

Subtract equation (3) from (2).

8x + 5y -(8x+6y)= 780-880

-y = -100

y = 100

Put the value of y in equation (1).

4x+3(100) = 440

4x = 440-300

4x = 140

x = 35

Hence, the value of x is 35 and that of y is 100.