We want to find out how much we will pay for our activities at a vacation resort. We do not know how much the activities themselves cost, but we do know how much two tourists paid to do the activities. Let's create a system of linear equations using this information and then solve it using the Elimination Method to find the costs of the activities.
Parasailing
Horseback Riding
Total Cost
Tourist 1
2 hours
5 hours
$ 205
Tourist 2
3 hours
3 hours
$ 240
We will use x to represent the cost per hour of parasailing and y to represent the cost per hour of horseback riding. From the table, we can see that the first tourist paid a total of $ 205 for 2 hours of parasailing and 5 hours of horseback riding. Let's write this as an equation.
2* x+ 5* y= 205The second tourist paid a total of $ 240 for 3 hours of parasailing and 3 hours of horseback riding.
3* x+ 3* y= 240
We have two equations that we can combine into a system of equations. Let's take a look.
2x+5y=205 & (I) 3x+3y=240 & (II)
Now we are ready to solve the system to find out how much each hour of the activities costs. Notice that no pair of like terms has the same or opposite coefficients. Let's multiply Equation (I) by 3 and Equation (II) by 2 so that the x-terms have the same coefficient.
If we subtract Equation (II) from Equation (I), the result is an equation in only one variable, y. We also could have multiplied either equation by a negative number and then added the equations — the answer would be the same.
We found that each hour of parasailing costs $ 65 and each hour of horseback riding costs $ 15. Finally, we can calculate how much we will have to pay for 1 hour of parasailing and 2 hours of horseback riding.
1* $65 + 2* $15=$95
We will pay $95 to go parasailing and horseback riding.
