Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A gardener is designing a rectangular flower bed with a perimeter of 40 feet. If the length of the flower bed is 4 feet longer than its width, what are the dimensions of the flower bed?
- AWidth = 9 feet, Length = 13 feet
- BWidth = 12 feet, Length = 16 feet
- CWidth = 8 feet, Length = 12 feet
- DWidth = 10 feet, Length = 14 feet
Show answer & explanationAnswer & explanation
Correct answer: C. Width = 8 feet, Length = 12 feet
Let 'w' be the width and 'l' be the length. We have two equations: l = w + 4 (length is 4 feet longer than width) and 2l + 2w = 40 (perimeter formula). Substitute the first equation into the second: 2(w + 4) + 2w = 40. Solve for 'w', then find 'l'.
Why the other options are wrong
- A. Incorrect. If width = 9, length = 13. Perimeter = 2(13) + 2(9) = 26 + 18 = 44, not 40.
- B. Incorrect. If width = 12, length = 16. Perimeter = 2(16) + 2(12) = 32 + 24 = 56, not 40.
- D. Incorrect. If width = 10, length = 14. Perimeter = 2(14) + 2(10) = 28 + 20 = 48, not 40.
Systems of Linear Equations
A set of two or more linear equations involving the same variables, whose solutions are points that satisfy all equations simultaneously.
- Can be solved by substitution, elimination, or graphing.
- A unique solution represents the intersection point of lines.
- No solution (parallel lines) or infinite solutions (same line) are possible.
Memory trick: Two lines meet, one solution sweet; substitution or elimination, choose your feat.