The city council has proposed a streetcar project for the downtown area.

Question

The cost of the streetcar project is x dollars.
The cost of the project is reduced by 15% if the project is not completed by the due date.
Which expressions can be used to determine the total cost of the project if the project is not completed by the due date?
Select all correct answers.
0.15x

0.85x

X - 0.85

X - 0.15x

X - 0.15

Answer 1

To determine the total cost of the streetcar project if it is not completed by the due date, we start with the original cost, \(x\). If the cost is reduced by 15%, we can express this mathematically.

1. Calculate the reduction: A 15% reduction of \(x\) can be expressed as \(0.15x\).
2. Calculate the new cost: The new cost after the reduction is given by the original cost minus the reduction: \[ \text{New Cost} = x - 0.15x = (1 - 0.15)x = 0.85x. \]

From this analysis, we can identify the correct expressions. The expressions that can be used to determine the total cost of the project if it is not completed by the due date are:

• 0.85x (This represents the cost after the 15% reduction.)
• X - 0.15x (This expression simplifies to 0.85x, representing the cost after the reduction.)

Therefore, the correct answers are 0.85x and X - 0.15x.

The other expressions, \(0.15x\), \(X - 0.85\), and \(X - 0.15\), do not represent the total cost after the 15% reduction.