Question

You meet some friends while traveling! You decide to go on An ATV tour. Tickets for a one-hour tour are $25 each. Tickets for a two-hour tour are $48. Your group bought a total of 8 tickets and spent a total of $315. How many of each type of ticket did your group buy?

Answer 1

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Interpret the statements

Let the tickets for a one-hour tour be represented by x

Let the tickets for a two-hour tour be represented by y

`\begin{gathered} It\text{ can be deduced from the statements in the question that;} \\ 25x+48y=313 \\ x+y=8 \end{gathered}`

STEP 2: Solve the derived equations simultaneously

`\begin{gathered} 25x+48y=313---\text{equation 1} \\ x+y=8----\text{equation 2} \\ \text{From equaton 2,} \\ x=8-y \\ \mathrm{Substitute\: }x=8-y\text{ into equation 1} \\ 25(8-y)+48y=315 \\ 200-25y+48y=315 \\ 200+23y=315 \\ 23y=315-200=115 \\ y=(115)/(23)=5 \end{gathered}`

STEP 3: Get the value of x

`\begin{gathered} \text{From equation 2} \\ x+y=8,x=8-y \\ \mathrm{Substitute\: }y=5 \\ x=8-5=3 \end{gathered}`

Hence,

the number of tickets for a one-hour tour bought is 3

the number of tickets for a two-hour tour bought is 5