Recognize that this problem can be solved with a system of
simultaneous equations. There are three methods we can use.
They are elimination, substitution and graphing. Let's use the
elimination method. Our strategy is to eliminate one of the two
variables in each equation and solve for the remaining variable.
Let...
r=horseback riding (1hour cost)
p=parasailing (1 hour cost)
Write the two equations from the problem statement info...
3r+2p=192......Eq1
2r+3p=213......Eq2
9r+6p=576.....equivalent Eq1, multiply Eq1 by 3
-4r -6p=-426....equivalent Eq2, multiply Eq2 by (-2)
---------------
5r =150......add each term in Eq1 and Eq2, note the
"p" term will cancel
∴ r=30.......divide both sides by 5
Now substitute 30 for "r" in either of Eq1 or Eq2. Let's use Eq1...
3(30)+2p=192...substitute for"r"
90+2p=102
∴ p=51.....divide both sides by 2
Let's check both values for truth in our original equations
Eq1, Eq2....
3(30)+2(51)=192.....Eq1, substitute values for "r" and "p"
90+103=192
192=192.....true, √check
2(30)+3(51)=213.....Eq2, substitute values for "r" and "p"
60+153=213
213=213.....true, √check
Both our values for "r" and "p" are correct. Always check
your solutions and work!
So the cost of horseback riding per hour is $30, and
the cost of parasailing per hour is $51.
Now attempt to solve this problem using the two other
methods mentioned above.
