The following problem appeared on the SAT. A cubic box with edge of length x inches is tied with a string 106 inches long. The string crosses itself at right angles on the top and bottom of the box. If the bow required 10 inches of string, what is the maximum number of inches x could be? 1. Write an equation based on this information. 2. Solve the equation for x. Solution:
1. The total length of the string is 106 inches, with the bow being 10 inches. Each side of the box is x inches. We can follow the string this way: Front face + top + back + bottom = 4x. Top face + right + bottom + left = 4x. So the total amount of string = 4x + 4 x = 8x. So we can write the equation as: 8x + 10 = 106 2. If 8x + 10 = 106, then: 8x = 106 10 = 96 Or, 8x = 96 or x = 96/8 = 12 So the length of the string without the box = 12 inches.
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