Chapter 4.2, Problem 32PPS

a.

To determine

To define the variables and write an equation in standard form.

Answer to Problem 32PPS

  $\Rightarrow 1.25x+2.00y=90$

Explanation of Solution

Given:

Cost of bus ride: $1.25

Cost of Train ride: $2.00

Monthly transportation cost: $90

Calculation:

Let x be the number of the bus rides and y be the number of the train rides.

This situation can be modelled as,

  $\Rightarrow 1.25x+2.00y=90$

Conclusion:

Therefore, the given situation is modelled as $1.25x+2.00y=90.$

b.

To determine

To calculate the number of train rides in the month.

Answer to Problem 32PPS

30

Explanation of Solution

Given:

Cost of bus ride: $1.25

Cost of Train ride: $2.00

Monthly transportation cost: $90

Given that the number of bus rides is 24.

From subpart (a),

  $\Rightarrow 1.25x+2.00y=90$

Calculation:

Let x be the number of the bus rides and y be the number of the train rides.

  $\Rightarrow 1.25x+2.00y=90$

Given that the number of bus rides is 24.

Substituting the value in the given equation,

  $\begin{array}{l}\Rightarrow 1.25(24)+2.00y=90\\ \Rightarrow 30+2.00y=90\\ \Rightarrow 2.00y=60\\ \Rightarrow y=30\end{array}$

Conclusion:

Therefore, the number of train rides in the month is 30.