OG详解-OG9 数学1 Q16

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 = 4y+6. Substituting 4y+6 for x in the equation x+y = 106 yields 4y+6+y = 106, or 5y+6 = 106. Subtracting 6 from each side of this equation yields 5y = 100. Dividing each side of this equation by 5 yields y = 20. Substituting 20 for y in the equation x = 4y+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.