A wire with a length of 106 inches is cut into two parts. One part has a length of x

Question

A wire with a length of 106 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 6 more than 4 times the value of y . What is the value of x ?

Accepted Answer

Choice D is correct. It's given that a wire with a length of 106 inches is cut into two parts. It's also given that one part has a length of x inches and the other part has a length of y inches. This can be represented by the equation x + y = 106 . It's also given that the value of x is 6 more than 4 times the value of y . This can be represented by the equation x = 4 y + 6 . Substituting 4 y + 6 for x in the equation x + y = 106 yields 4 y + 6 + y = 106 , or 5 y + 6 = 106 . Subtracting 6 from each side of this equation yields 5 y = 100 . Dividing each side of this equation by 5 yields y = 20 . Substituting 20 for y in the equation x = 4 y + 6 yields x = 4 ( 20 ) + 6 , or x = 86 . Choice A is incorrect. This value represents less than half of the total length of 106 inches; however, x represents the length of the longer part of the wire, since it's given that the value of x is 6 more than 4 times the value of y . Choice B is incorrect. This value represents less than half of the total length of 106 inches; however, x represents the length of the longer part of the wire, since it's given that the value of x is 6 more than 4 times the value of y . Choice C is incorrect. This represents a part that is 6 more than the length of the other part, rather than 6 more than 4 times the length of the other part.

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