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If y varies directly as x and y = 198 when x = 22, how do you find y when x = 182?

Answer 1

Abigail Allen

#y = 1638#

"#y# varies directly as #x#" tells us that for some constant (some number) #k#, we have"

#y = kx#

We are also told that #y = 198# when #x = 22#.

We can use this to find the number #k#.

#198 =k*22# so

#k = 198/22 = (11*18)/(11*2) = 18/2 =9#

So we have learned that #y = 9x#

Now, when #x=182#, we must have #y = 9(182)# So #y = 1638#

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Answer 2

Isaiah Anthony

You can use cross multiplication.

#y_1/x_1=y_2/x_2#, where #y_1=198;# #x_1=22;# #y_2=?;# #x_2=182#.

#198/22=y_2/182#

Cross multiply.

#(198*182)/(22)=y_2#

#1368=y_2#

Switch sides.

#y_2=1368#

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Answer 3

Jameson Allen

To find ( y ) when ( x = 182 ), use the direct variation formula ( y = kx ), where ( k ) is the constant of variation.

First, find ( k ) using the given values: ( y = 198 ) when ( x = 22 ).
Substitute these values into the formula to solve for ( k ): ( 198 = k \times 22 ).
Solve for ( k ): ( k = \frac{198}{22} ).
Once you have ( k ), substitute it into the direct variation formula with the new value of ( x ) to find ( y ): ( y = k \times 182 ).

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