Chapter 5.4, Problem 32E

To determine

To explain:

Friend says she can determine the exact cost of one admission and one skate rental.

Answer to Problem 32E

There is infinite many solution that means there is not enough formation to find out cost of admission.

Explanation of Solution

Given information:

  

For the first group, it is given that for $3$ peoples paid admission and $2$ people got skate rentals.

The total amount o money the group sent was $\$38$ .

This is represented by the equation,

  $3x+2y=\mathrm{38...}\left(i\right)$

For the second group, it is given that for $15$ peoples paid admission and $10$ people got skate rentals.

The total amount of money the group sent was $\$190$ .

This is represented by the equation,

  $15x+10y=\mathrm{190...}\left(ii\right)$

Both these equations represents same lines, for checking it multiply by $5$ on both sides,

  $\begin{array}{l}5.3x+5.2y=5.38\\ 15x+10y=\mathrm{190...}\left(iii\right)\end{array}$

  $15x+10y=190$ is a result of multiplying both sides of first equation by $5$ .

It is become same equation as he second equation.

So it is conclude that there is infinitely many solution that means there is not enough formation to find out cost of admission.