Question

Jason owns a small textile company that produces shirts. On a particular day, Jason has one worker come into the shop to make shirts. He must pay the worker $25 per hour and also pay $1.75 per shirt for material costs. The worker created an average of 5 shirts per hour and Jason's total expenses for labor and materials were $270. Write a system of equations that could be used to determine the number of hours the worker worked and the number of shirts the worker made. Define the variables that you use to write the system.

Answer 1

Variables:

`x` → The number of hours the worker worked

`y` → The number of shirts the worker made.

System fo equations:

`\left \{ {{25x+1.75 y=270} \atop {y=5x}} \right.`

Explanation:

Let be
`x` the number of hours the worker worked and
`y` the number of shirts the worker made.

Since:

• Jason must pay the worker $25 per hour (which can be represented with
  `25x`).
• He must pay $1.75 per shirt for material costs (which can be represented with
  `1.75y`).
• The total expenses were $270.

You can write the following equation:

`25x+1.75 y=270`

Knowing that the worker created an average of 5 shirts per hour, you can write the other equation:

`y=5x`

Therefore, with this equations you can set up the following system of equations, which could be used to determine the number of hours the worker worked and the number of shirts the worker made:

`\left \{ {{25x+1.75 y=270} \atop {y=5x}} \right.`