Question

Jake and Joshua have new jobs selling gift cards at a local convenience store at the cash register, but their pay is different. Jake earns a foundational wage of $6 per hour, as well as $8 for each gift card sold. Joshua gets $4 for each gift card sold and earns a foundational wage of $6 per hour. If they each sell a certain number of gift cards in one hour, they will end up earning the same amount of pay. How many gift cards would that make up to?Write a system of equations, graph them, and type the solution.

Answer 1

Let x be the number of cards Jake and Joshua sell within one hour. Therefore, their earnings are given by the following expressions,

`\begin{gathered} Ja=6+8x \\ Jo=6+4x \end{gathered}`

Then, set Ja=Jo (both earn the same amount),

`\begin{gathered} Ja=Jo \\ \Rightarrow6+8x=6+4x \end{gathered}`

Solving for x,

`\begin{gathered} \Rightarrow8x=4x \\ \Rightarrow4x=0 \\ \Rightarrow x=0 \end{gathered}`

Then, they will earn the same within one hour only if both sell zero cards within the hour.

Graphing the system of equations,

As one can see, the intersection point is (0,6), which stands for 0 cards and $6