Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A rectangular garden has a length that is 5 feet more than twice its width. If the area of the garden is 150 square feet, which equation can be used to find the width (w) of the garden?
- A2w + 5 = 150
- Bw(w + 5) = 150
- C2w + 2(2w + 5) = 150
- Dw(2w + 5) = 150
Show answer & explanationAnswer & explanation
Correct answer: D. w(2w + 5) = 150
Let the width be 'w'. The length 'l' is 5 feet more than twice its width, so l = 2w + 5. The area of a rectangle is length * width. So, w * (2w + 5) = 150.
Why the other options are wrong
- A. Incorrect. This is an incomplete representation of the relationship and does not involve area or multiplication of dimensions.
- B. Incorrect. This assumes length is 'w + 5', not '2w + 5'.
- C. Incorrect. This represents the perimeter, not the area, and it's equated to 150 square feet, which is an area.
Translating Word Problems to Equations
The process of converting a real-world scenario described in words into a mathematical equation or set of equations.
- Assign variables to unknown quantities.
- Identify keywords that indicate mathematical operations (e.g., 'is' for equals, 'more than' for addition).
- Break down complex sentences into smaller, manageable parts.
- Formulate equations that accurately represent the given relationships.
Memory trick: Read, define, translate, equation: the four steps to problem creation.