Question

How much does a student pay to use the telescope for one hour?

Answer 1

Let x be how much student pays for one hour to use the telescope

Let y be how much student pays for one hour to use the supercomputer.

Equation for student 1:

`5x+3y=70.50`

Equation for student 2:

`6x+2y=67.00`

Use both equations above as a system of equations to solve x:

1. Solve y in the equation for student 1:

`\begin{gathered} 3y=70.50-5x \\ \\ y=(70.50)/(3)-(5)/(3)x \\ \\ y=23.5-(5)/(3)x \end{gathered}`

2. Substitute the y in the second equation by the value you get in step 1:

`6x+2(23.5-(5)/(3)x)=67.00`

3. Solve x:

`\begin{gathered} 6x+47-(10)/(3)x=67.00 \\ \\ 6x-(10)/(3)x=67.00-47 \\ \\ (18x-10x)/(3)=20.00 \\ \\ (8)/(3)x=20.00 \\ \\ 8x=3\cdot20.00 \\ \\ 8x=60.00 \\ \\ x=(60.00)/(8) \\ \\ x=7.5 \end{gathered}`

Then, A student pays $7.5 to use the telescope for one hour