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?
","rationale_html":"Choice B is correct. It’s given that the ratio of the rectangular region’s length to its length=35 =35 width is 35 to 10. This can be written as a proportion: , or . This width 10 w 10 = = proportion can be rewritten as 10 35w, or 3.5w. 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 with + + + = ( +) x and w with w 7 in the equation, which gives 3.5x 7 .w This + = + equation can be rewritten using the distributive property as 3.5x 24w.5. 38 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 1 = Since 3.5w, the right-hand side of this equation can be rewritten by + = + = substituting for 3.5w, which gives x 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.
","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"It must decrease by 24.5 units.
","ord":0},{"label":"B","content_html":"It must increase by 24.5 units.
","ord":1},{"label":"C","content_html":"It must decrease by 7 units.
","ord":2},{"label":"D","content_html":"It must increase by 7 units.
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