For a certain rectangular region, the ratio of its length to its width is 35 to 10 . If the

Question

For a certain rectangular region, the ratio of its length to its width is 35 to 10 . If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?

Accepted Answer

Choice B is correct. It&rsquo;s given that the ratio of the rectangular region&rsquo;s length to its width is 35 to 10 . This can be written as a proportion: length width = 35 10 , or l w = 35 10 . This proportion can be rewritten as 10 l = 35 w , or l = 3.5 w . If the width of the rectangular region increases by 7 , then the length will increase by some number x in order to maintain this ratio. The value of x can be found by replacing l with l + x and w with w + 7 in the equation, which gives l + x = 3.5 w + 7 . This equation can be rewritten using the distributive property as l + x = 3.5 w + 24.5 . Since l = 3.5 w , the right-hand side of this equation can be rewritten by substituting l for 3.5 w , which gives l + x = l + 24.5 , or x = 24.5 . Therefore, if the width of the rectangular region increases by 7 units, the length must increase by 24.5 units in order to maintain the given ratio. Choice A is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease. Choice C is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease. Choice D is incorrect. Since the ratio of the length to the width of the rectangular region is 35 to 10 , if the width of the rectangular region increases by 7 units, the length would have to increase by a proportional amount, which would have to be greater than 7 units.

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