Question

Jake and Joshua go to different festivals during the day. Jake must pay a fee of $10 for a ticket and additional 1$ for every food/beverage. Joshua has to pay 5$ for a ticket and additional 4$ for the food and drinks. How many beverages and food would it take for Joshua to have the same amount of pay as Jake? Graph the item.Write a system of equations, graph them, and type the solution.

Answer 1

Let x be the number of beverages and food; therefore, the two equations that model Jack's and Joshua's expenditures are

`\begin{gathered} Ja=10+1x \\ Jo=5+4x \end{gathered}`

In order to graph both linear equations, we need two points on each of them. Finding the points,

`\begin{gathered} x=0\Rightarrow Ja=10+1\cdot0=10 \\ (0,10) \\ x=1\Rightarrow Ja=10+1\cdot1=11 \\ \Rightarrow(1,11) \\ \text{and} \\ x=0\Rightarrow Jo=5+4\cdot0=5 \\ \Rightarrow(0,5) \\ x=1\Rightarrow Jo=5+4\cdot1=9 \\ \Rightarrow(1,9) \end{gathered}`

Therefore, the graph of the two lines simultaneously is

The intersection point is (5/3, 35/3). Therefore, the answer is 5/3 beverages and food