The perimeter of a rectangular booth at the craft festival must be at least 58 feet. The width of JOhn's booth is 7 1/2 feet. What lengths of the rectangle will meet the required perimeter?
1. Define variable and write and inequality
2. Solve the inequality
3. Graph the solution
4. Explain the solution in words
2(7.5+x) >= 58
Surely there is a maximum though, eh?
1. Define variable and write an inequality:
Let's define the length of the rectangular booth as "L". The given width of John's booth is 7 1/2 feet. The perimeter of a rectangle is calculated by adding all the sides, so the inequality representing the required perimeter can be written as follows:
2L + 2(7.5) ≥ 58.
2. Solve the inequality:
Let's simplify the equation by distributing and combining like terms:
2L + 15 ≥ 58.
Subtract 15 from both sides to isolate the variable:
2L ≥ 43.
Now, divide both sides of the equation by 2 to solve for the length:
L ≥ 43/2.
3. Graph the solution:
To graph the solution on a number line, we start by marking the inequality as a solid line at 43/2. Since the inequality is "L ≥ 43/2," we shade the line to the right side since we want lengths greater than or equal to 43/2.
4. Explain the solution in words:
The solution to the inequality is that the length of the rectangular booth must be greater than or equal to 43/2 feet (or 21.5 feet). So, any length equal to or greater than 21.5 feet will meet the required perimeter of at least 58 feet when combined with the given width of 7 1/2 feet.