Final answer:
A real-world scenario to use system of equations is determining the number of pens and notebooks one can buy on a fixed budget with a minimum item requirement. By identifying the unknowns, knowns, and setting up two equations based on price and item constraints, the equations can be solved to find a solution that aligns with the budget and item quantity.
Step-by-step explanation:
To illustrate a real-world scenario where you would use a system of equations to solve, consider the following example:
- You want to purchase a combination of pens and notebooks for school supplies. The pens cost $1.50 each, and the notebooks cost $3.50 each.
- Your budget is $20, and you need to buy at least 10 items in total.
Identify the unknowns: Let x represent the number of pens and y represent the number of notebooks.
Identify the knowns: The price of pens ($1.50), the price of notebooks ($3.50), and the total amount to spend ($20).
You can set up two equations: 1.5x + 3.5y = 20 (budget constraint) and x + y = 10 (item constraint).
Solve the equations by using substitution or elimination methods to find the values of x and y that satisfy both equations simultaneously. After solving, you obtain numerical solutions for the number of pens and notebooks you can buy within your budget.