Question

The cost for 2 adults and 3 children on horse ride is \[\$14\]. If each child’s fare is one-half of each adult’s fare, find the total cost for one adult and one child.
A. \[\$ 4.00\]
B. \[\$ 5.25\]
C. \[\$ 6.00\]
D. \[\$ 6.50\]

Answer 1

Hint: In this problem, first we need to find the cost of horse ride for one adult and one child in a single variable. Next, multiply the cost of one adult by 2 and one child by 3 and add them. Now, put the obtained sum equal to 14 and solve.

Complete step by step answer:
Consider the cost of a horse ride for one adult be \[x\].
Since, a child’s fare is one-half of an adult's fare, the cost of horse ride for one child will be \[\dfrac{x}{2}\].
Now, the cost for 2 adults and 3 children on horse ride is \[\$14\], therefore,
\[
  \,\,\,\,\,\,\,2\left( x \right) + 3\left( {\dfrac{x}{2}} \right) = 14 \\
   \Rightarrow 2x + \dfrac{{3x}}{2} = 14 \\
   \Rightarrow \dfrac{{4x + 3x}}{2} = 14 \\
   \Rightarrow \dfrac{{7x}}{2} = 14 \\
\]
Further, solve the above equation, to obtain the value of \[x\].
\[
  \,\,\,\,\,\,\,7x = 14 \times 2 \\
   \Rightarrow 7x = 28 \\
   \Rightarrow x = \dfrac{{28}}{7} \\
   \Rightarrow x = \$ 4 \\
\]
Now, the total cost of one adult and one child is calculated as shown below.
\[
  \,\,\,\,\,\,x + \dfrac{x}{2} \\
   \Rightarrow 4 + \dfrac{4}{2} \\
   \Rightarrow 4 + 2 \\
   \Rightarrow \$ 6 \\
\]

So, the correct answer is “Option C”.

Note: A linear equation in one variable has one solution. The solution of the linear equation represents the point intersection on the \[x\] axis.