Question

A resort in Orlando, Florida offers vacationers two boat ride plans. Plan A gives 3 nights lodging and 5 boat rides for a total cost of $625. Plan B gives 5 nights lodging and 6 boat rides for a total of $960What is the cost of each boat ride?

Answer 1

Given is Plan A gives 3 nights lodging and 5 boat rides for a total cost of $625.

and Plan B gives 5 nights lodging and 6 boat rides for a total of $960.

Let x be the cost of night lodging and y be the cost of the boat ride.

The given can be written as follows.

$3x+5y=625$$5x+6y=960$

Multiply equation 3x+5y=625 by 5 as follows.

$5\times3x+5\times5y=5\times625$

$15x+25y=3125\text{ take it as equation (1).}$

Multiply equation 5x+6y=960 by 3 as follows.

$3\times5x+3\times6y=3\times960$

$15x+18y=2880\text{ take this as equation (2).}$

Substract equation (2) from equation (1) to compute the value of y.

$(15x+25y)-(15x+18y)=3125-2880$

$15x+25y-15x-18y=3125-2880$

Solve like terms.

$7y=245$

Dividing by 7 into both sides, we get

$\frac{7y}{7}=\frac{245}{7}$

$y=35$

Hence we get the cost of the boat ride is $35.

Substitute y=35 in 3x+5y=625 to compute the value of y.

$3x+5(35)=625$

$3x+175=625$

Adding -175 on both sides, we get

$3x+175-175=625-175$

Solve like terms.

$3x=450$

Dividing by 3 into both sides, we get

$\frac{3x}{3}=\frac{450}{3}$

$x=150$

Hence the cost of night lodging is $150.

Result :

The cost of night lodging is $150.

The cost of the boat ride is $35.

The cost of each boat is $150 and $35.