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1. Suppose y varies inversely with x, and y = 9 when x = 6. What is an equation for the inverse variation?

Problem 2 Using Inverse Variation

GRIDDED RESPONSE

Physics The weight needed to balance a lever varies inversely with the distance from the fulcrum to the weight. How far away from the fulcrum should the person sit to balance the lever?

Relate The 1000-lb elephant is 7 ft from the fulcrum. The 160-lb person is x ft from the fulcrum. Weight and distance vary inversely.

Define Let weight 1 = 1000  lb . Let distance 1 = 7  ft . Let weight 2 = 160  lb . Let distance 2 = x  ft . table with 2 rows and 1 column , row1 column 1 , cap letweight sub 1 . equals , 1000 , lb . . . cap letdistance sub 1 . equals 7 ft . . . cap letweight sub 2 . equals 160 , lb . , row2 column 1 , cap letdistance sub 2 . equals x ft . , end table

Write weight 1 ⋅ distance 1 = weight 2 ⋅ distance 2   1000 ⋅ 7 = 160 ⋅ x Substitute .     7000 = 160 x     Simplify .     43.75 = x     Divide each side by  160. table with 4 rows and 8 columns , row1 column 1 , weight sub 1 , column 2 dot , column 3 distance sub 1 , column 4 equals , column 5 weight sub 2 , column 6 dot , column 7 distance sub 2 , column 8 , row2 column 1 , 1000 , column 2 dot , column 3 7 , column 4 equals , column 5 160 , column 6 dot , column 7 x , column 8 cap substitute . . , row3 column 1 , , column 2 , column 3 7000 , column 4 equals , column 5 160 x , column 6 , column 7 , column 8 cap simplify , . , row4 column 1 , , column 2 , column 3 43.75 , column 4 equals , column 5 x , column 6 , column 7 , column 8 cap divideeachsideby . 160. , end table

The person should sit 43.75 ft from the fulcrum to balance the lever.

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2. A 120-lb weight is placed on a lever, 5 ft from the fulcrum. How far from the fulcrum should an 80-lb weight be placed to balance the lever?