Question

apply: rewriting expressions
a comic book increased in value by 5% over the last year.
which two expressions can be used to find the increased value of the comic book when given the original value, x?
click or tap each correct answer.
1.5x
1.05x
(1 - 0.05)x
1 + 0.05x
(1 + 0.05)x

Explanation:

Step1: Understand the problem

A comic book's value increased by 5% over last year. Let the original value be \( x \). We need to find the expressions that represent the increased value.

Step2: Recall percentage increase formula

The formula for a percentage increase of \( r\% \) on a value \( x \) is \( x + r\% \times x = x(1 + \frac{r}{100}) \). Here, \( r = 5 \), so \( \frac{r}{100} = 0.05 \).

Step3: Analyze each expression

• \( 1.5x \): This represents a 50% increase (since \( 1.5 = 1 + 0.5 \)), not 5%. So incorrect.
• \( 1.05x \): Using the formula, \( x(1 + 0.05)=1.05x \). Correct.
• \( (1 - 0.05)x \): This is a 5% decrease (since we subtract 0.05), not increase. Incorrect.
• \( 1 + 0.05x \): This is \( 1 + \) (5% of \( x \)), which is not the correct form for the total value. The total value should be \( x + 0.05x \), not \( 1 + 0.05x \). Incorrect.
• \( (1 + 0.05)x \): Simplifying \( (1 + 0.05)x = 1.05x \), which is the same as the correct formula. Correct.

Answer:

1.05x, (1 + 0.05)x