Question

The 1996 Summer Olympics are to be held in Atlanta, Georgia. In 1991, the planned budget for the event was $1,162,000. The budget contained three categories: operating expenses (e), facilities construction (c), and surplus (s). The amount allowed for operating expenses was the same as the total amount allowed for facilities construction and surplus combined. The budget committee estimated that 14% of the total budget would be surplus. Write a linear system that represents this information. Solve the linear system to find the amount of money budgeted for each category.

Answer 1

The linear system based on the budget for the 1996 Summer Olympics includes equations for operating expenses, facilities construction, and surplus. By solving the equations, the amounts budgeted are $499,660 for operating expenses, $499,660 for facilities construction, and $162,680 for surplus.

Step-by-step explanation:

The student is asked to write and solve a linear system based on the given budget information for the 1996 Summer Olympics. The budget is $1,162,000, with operating expenses (e), facilities construction (c), and surplus (s) as categories. The conditions are that operating expenses are equal to the sum of facilities construction and surplus combined, and the surplus is 14% of the total budget.

To represent this information as a linear system, we can set up the following equations:

1. e = c + s
2. s = 0.14 × 1,162,000
3. e + c + s = 1,162,000

Substituting equation (2) into equation (3) and using equation (1), we can solve for each variable.

Solving the system, we find:

• s = $162,680 (surplus)
• e = $499,660 (operating expenses)
• c = $499,660 (facilities construction)