Question

Solve the following problems using inverse functions: 1. A bus ride costs PhP 10.00 for the first 5 kilometers, and its additional integer kilometer adds PhP 1.75 to the fare. How far can you reach if you have Php 185.00 budget for the fare? 2. Jeenay, a sales agent, earns PhP 17,000.00 monthly plus 18?

Answer 1

1. You can reach approximately 91.43 kilometers with a budget of PhP 185.00 for the bus fare.

2. Jeenay's total monthly earnings amount to PhP 17,444.44, including the fixed amount of PhP 17,000.00 plus 18% of the additional sales.

Step-by-step explanation:

For the first problem, let's define the distance traveled (in kilometers) as

( x ) and the total cost (in PhP) as ( y ). The cost function can be represented as
`\( y(x) = 10 + 1.75(x-5) \) for \( x > 5 \)`(since the first 5 kilometers have a fixed cost of PhP 10.00). To find the distance for a given budget of PhP 185.00, we set ( y(x) = 185.00 ) and solve for ( x ):

185.00 = 10 + 1.75(x-5)

Solving this equation yields ( x = 91.43 ) kilometers, rounding to two decimal places.

For the second problem, Jeenay's total monthly earnings ( y ) can be expressed as a function of the additional sales ( x ): ( y(x) = 17,000 + 0.18x). To find the total earnings when the additional sales are at their maximum, we substitute
`\( x = (17,000)/(0.18) \):`

`\[ y = 17,000 + 0.18 * (17,000)/(0.18) = 17,444.44 \]`

Therefore, Jeenay's total monthly earnings, including the fixed amount and additional sales commission, amount to PhP 17,444.44.