If y varies inversely with x and y = 6 when x = 3, then what is y when x = 2?

Question

i need help figuring out this problem

Answer 1

WHEN YOU HAVE A DIRECT PROPORTION YOU WOULD SET UP FRACTIONS AND CROSS MULTIPLY

 

X/Y = A/B

 

FOR AN INVERSE PROPORTION YOU CAN MULTIPLY YOUR TERMS AND SET THEM EQUAL

XY=AB

 

iN YOUR QUESTION JUST PLUG IN THE X'S AND Y'S YOU HAVE.  USUALLY THE FIRST SENTENCE OR PART OF THE QUESTION WILL JUST BE THE LEFT SIDE OF THE EQUATION.  W/E INFO THEY GIVE YOU WILL GO IN THE RIGHT.  SINCE THEY ARE ASKING FOR Y, DONT PLUG ANYTHING IN FOR IT ON THE RIGHT BC YOU ARE GOING TO SOLVE FOR IT

XY=XY

(3)(6)=2Y

 

18=2Y

Y=9

 

 

+++THE OTHER TWO ANSWERS ABOVE ARE ALSO CORRECT, JUST DO WHAT YOU FEEL MOST COMFORTABLE WITH

Answer 2

When a variable y inversely varies with another x, it means that when y is doubled x is halved, when y is tripled x reduces to a third of original value.  This is shown below:

 

Suppose x is 4 when y is 2, then x is halved 2 when y doubled to 4.  When x is reduced to 1 (1/4th of the original value) then y is multiplied 4 times the original value to 2*4 = 8

 

In other words, x*y remains constant, which in the above example is 4*2.  

 

With the background above, we can answer the question

 

It is given in the question that y is 6 when x is 3.

 

Since y varies inversely with x, we know that x*y is constant which in this case is 6*3 = 18

 

When x changes to 2 y = 18/x =9  (since we know x*y = 18)

Answer 3

Since y varies inversely with x, we have:

y = a/x

y = 6 and x = 3

6 = a/3

6*3 = 3*a/3

18 = a

y = 18/x

 

When x = 2

y = 18/2 = 9