Chapter 6.3, Problem 39PPE

To determine

To calculate: cost of 1 h of each activity.

Answer to Problem 39PPE

Cost of 1 h of horseback riding is $\$30$ and parasailing is $\$51$ .

Explanation of Solution

Given information: A hotel offers two activity packages. One costs $\$192$ and includes 3h of horseback riding and 2h of parasailing. The second costs $\$213$ and includes 2h of horseback riding and 3h of parasailing.

Calculation:

Let’s assume rate of 1h of horseback riding is $ $x$ and parasailing is $ $y$ .

the first package is of $\$192$ which includes 3h of horseback riding and 2h of parasailing.

  $\therefore 3x+2y=192$.....(i)

the second package is of $\$213$ which includes 2h of horseback riding and 3h of parasailing.

  $\therefore 2x+3y=213$.....(ii)

Multiply equation (i) with 2 and equation (ii) with 3 and subtract (ii) from (i),

  $6x+4y=384$

  $\underset{\_}{\_6x+9y=639}$

  $-5y=-255$

  $\therefore y=51$

Let’s put the value of $y$ in second equation,

  $\therefore x=30$