Math Problems in Direct Variation? Any Help? 10 points best answer

The income ( I ) of a worker earning k dollars per hour varies directly as the number of hours ( h ) he works.

Find k, if y varies directly as x and:

1.) y = 24 when x = 3
2.) y = 4 when x = 5 1/3
3.) x = 15 when y = 120
4.) x = 8 when y = 96
5.) x = 42 when y = 14
6.) x = 9 when y = 21

and these ones also:

1.) If y varies directly as x, and y = 40 when x= 16, find y when x = 30
2.) If y varies directly as x, and y = 45 when x = 2 1/2 , find x when y = 180
3.) If p varies directly as q, and p = 25 when q = 20, find q when p = 140

Thanks! I'll wait for your answers

Since no.of hours(h) is independent, therefore it lies in X-axis and income(I) is dependent variable so it lies on y-axis.
Therefore k=y/x[This is so because the worker is paid the amount i.e y which is the product of no.of hours(x) and k]
So
1) k=24/3=8
2)k=4/(51/3)=4/17
3)k=120/15=8
4)k=96/8=12
5)k=14/42=0.33333
6)k=21/9=7/3

also the other answers are
1)When x=16 then y=40
so when x=1, then y=40/16
therefore when x=30, then y=(40*30)/16=75
This method is called unitary method

the other problems can be solved by this method, the answers are:

2)When y=45, then x=21/2
when y=1, x= 21/(2*45)=7/30
when y=180, x=(7/30)*180=42

3) when p=25, then q=20
when p=1, then q=20/25=4/5
when p=140, then q=(4/5)*140=112

You are most welcome.....

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