QuestionAugust 25, 2025

6. A 42-inch string is to be cut so that one piece is 7 inches longer than the other. What is the length of the shorter piece? The shorter piece has a length of __ inches.

6. A 42-inch string is to be cut so that one piece is 7 inches longer than the other. What is the length of the shorter piece? The shorter piece has a length of __ inches.
6. A 42-inch string is to be cut so that one piece is 7 inches longer than the
other. What is the length of the shorter piece?
The shorter piece has a length of __ inches.

Solution
4.3(179 votes)

Answer

17.5 inches Explanation 1. Define Variables Let the length of the shorter piece be x inches. Then, the longer piece is x + 7 inches. 2. Set Up Equation The total length of both pieces is 42 inches. So, x + (x + 7) = 42. 3. Solve for x Simplify and solve: 2x + 7 = 42 \implies 2x = 35 \implies x = 17.5.

Explanation

1. Define Variables<br /> Let the length of the shorter piece be $x$ inches. Then, the longer piece is $x + 7$ inches.<br /><br />2. Set Up Equation<br /> The total length of both pieces is 42 inches. So, $x + (x + 7) = 42$.<br /><br />3. Solve for x<br /> Simplify and solve: $2x + 7 = 42 \implies 2x = 35 \implies x = 17.5$.
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