The total fare for two adults and three children on a boat is $14. If the child's fare is half of the adult's, what is the adult fare?

The total fare for two adults and three children on a boat is $14. If the child's fare is half of the adult's, what is the adult fare?

• A. $2.00
• B. $3.00
• C. $3.50
• D. $4.00

Answer: (D)

To determine the adult fare, we start by defining the cost per adult and the cost per child. Let’s define the adult fare as \( x \). According to the problem, the child's fare is half that of the adult fare, which can be expressed as \( \frac{x}{2} \). Given that there are two adults and three children, we can set up the following equation to represent the total fare: \[ 2 \times x + 3 \times \frac{x}{2} = 14 \] To simplify this equation: 1. Calculate the total fare for the children: - The fare for three children is \( 3 \times \frac{x}{2} = \frac{3x}{2} \). 2. Then, substitute this back into the equation: \[ 2x + \frac{3x}{2} = 14 \] 3. To eliminate the fraction, multiply the entire equation by 2: \[ 2(2x) + 2\left(\frac{3x}{2}\right) = 2(14) \] This simplifies to: \[ 4x + 3x = 28 \] 4. Combine like terms

To determine the adult fare, we start by defining the cost per adult and the cost per child. Let’s define the adult fare as ( x ). According to the problem, the child's fare is half that of the adult fare, which can be expressed as ( \frac{x}{2} ).

Given that there are two adults and three children, we can set up the following equation to represent the total fare:

[

2 \times x + 3 \times \frac{x}{2} = 14

]

To simplify this equation:

1. Calculate the total fare for the children:

• The fare for three children is ( 3 \times \frac{x}{2} = \frac{3x}{2} ).

2. Then, substitute this back into the equation:

[

2x + \frac{3x}{2} = 14

]

3. To eliminate the fraction, multiply the entire equation by 2:

[

2(2x) + 2\left(\frac{3x}{2}\right) = 2(14)

]

This simplifies to:

[

4x + 3x = 28

]

4. Combine like terms