Question

write an equation
we can use equations to represent relationships involving percent increase and decrease.
each new rectangle is 21% longer than the original.
write an equation to represent the relationship between the length of an original rectangle, b, and the length of the new rectangle, c.
(image shows three rectangles with lengths 120 cm, 50 cm, 150 cm, each with 100% and 21% segments)

Explanation:

Step1: Understand Percent Increase

A 21% increase means the new length is the original length plus 21% of the original length. Mathematically, 21% as a decimal is 0.21. So the increase is \( 0.21b \), and the new length \( c \) is original \( b \) plus the increase.

Step2: Formulate the Equation

The original length is \( b \). The new length \( c \) is \( b + 0.21b \), which can be factored as \( b(1 + 0.21) \). Calculating \( 1 + 0.21 \) gives \( 1.21 \). So \( c = 1.21b \).

Answer:

\( c = 1.21b \)