Chapter 6.4, Problem 27PPS

a.

To determine

To define the variable and write the system of linear equations for the given situation

Answer to Problem 27PPS

  $16x+3y=44.81$

  $22x+5y=67.73$

Explanation of Solution

Given:

For group A, there were 22 trips to batting cage and 5 golf games and the total price comes out to be $67.73.

For group B, there were 16 trips to batting cage and 3 golf games and the total price comes out to be $44.81.

Calculation:

Let,

The price of a trip to batting cage be $ x and the price of a golf game be $ y .

For group A, there were 22 trips to batting cage and 5 golf games and the total price comes out to be $67.73, which means,

  $16x+3y=44.81$

For group B, there were 16 trips to batting cage and 3 golf games and the total price comes out to be $44.81, which means

  $22x+5y=67.73$

Let,

  $16x+3y=\mathrm{44.81.......}(i)$

  $22x+5y=\mathrm{67.73.......}(ii)$

Conclusion:

Therefore, the system of equations are: $16x+3y=44.81$ and $22x+5y=67.73$.

b.

To determine

To solve the system of equation and explain the solution

Answer to Problem 27PPS

  $x=1.49$ and $y=6.99$.

Explanation of Solution

Given:

From sub part (a),

  $\begin{array}{l}16x+3y=44.81\\ 22x+5y=67.73\end{array}$

Calculation:

Let,

  $16x+3y=\mathrm{44.81.......}(i)$

  $22x+5y=\mathrm{67.73.......}(ii)$

Now, subtract $3\times$ equation (ii) from $5\times$ equation ( i ),

  $\begin{array}{l}\Rightarrow 5(16x+3y)-3(22x+5y)=5\times 44.81-3\times 67.73\\ \Rightarrow 80x+15y-66x-15y=20.86\\ \Rightarrow 14x=20.86\\ \Rightarrow x=1.49\end{array}$

Putting the value of x in equation ( i ),

  $\begin{array}{l}\Rightarrow 16\times 1.49+3y=44.81\\ \Rightarrow 23.84+3y=44.81\\ \Rightarrow 3y=20.97\\ \Rightarrow y=6.99\end{array}$

  $x=1.49$, it means that, the cost of one batting cage is $1.49.

  $y=6.99$, it means that, the cost of one golf game is $6.99.

Conclusion:

Hence, the solution of the system of equations is: $x=1.49$ and $y=6.99$ .