Question

One year ago, a cell phone model cost $p. Today, the cost of the cell phone model, in dollars, can be represented by the given expression.

0.93p

Which set of statements is true?
A.
The cost of the cell phone model increased by 93%.
An equivalent expression that represents this situation is p + 0.93p.
B.
The cost of the cell phone model increased by 7%.
An equivalent expression that represents this situation is p + 0.07p.
C.
The cost of the cell phone model decreased by 93%.
An equivalent expression that represents this situation is p − 0.93p.
D.
The cost of the cell phone model decreased by 7%.
An equivalent expression that represents this situation is p − 0.07p

Answer 1

To analyze the given information, let's break down the expression \(0.93p\):

- The current price of the cell phone model is \(0.93p\), which means it is 93% of the original price \(p\).
- This indicates a decrease from the original price \(p\), as \(0.93p\) is less than \(p\).

Now, let's determine how much the price has decreased:

1. The decrease is calculated as follows:
\[
\text{Decrease} = p - 0.93p = 0.07p
\]

2. To find the percentage decrease, we can compute it as:
\[
\text{Percentage Decrease} = \frac{\text{Decrease}}{\text{Original Price}} \times 100 = \frac{0.07p}{p} \times 100 = 7\%
\]

Now let's evaluate the options provided:

- **Option A** states that the cost increased by 93%. This is incorrect.
- **Option B** states that the cost increased by 7%. This is incorrect; the cost actually decreased.
- **Option C** states that the cost decreased by 93%. This is incorrect; the decrease is only 7%.
- **Option D** states that the cost decreased by 7%. This is correct.

The expression given for the decrease is also correct:
\[
p - 0.07p = 0.93p
\]

Thus, the correct option is:

**D. The cost of the cell phone model decreased by 7%. An equivalent expression that represents this situation is \(p - 0.07p\).**