Question

16- Your total pay y is proportional to the number of hours x that you work....

16- Your total pay y is proportional to the number of hours x that you work. Suppose in 2 hours your wage is $24.

a) Write an equation that represents the situation described above.

b) How many hours must you work to earn $192?

c) Is the equation you found in part (a) represent a mathematical or statistical model? Explain.

Math   Statistics-And-Probability   
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Answer #1

a) Given total pay, y is proportional to number of hours, x you work, In mathematical way, it can be written as -

y = kx , where k is constant of proportionality

Also, given in x = 2 hours, wage, y = $24

So, 24 = k(2) or k = 12

Therefore, the equation becomes, y = 12x

b) To earn y = $192, we need to find out number of hours of work i.e. x

Putting y = $192 in above equation :

192 = 12x

x = 192/12 = 16 , so one needs to work for 16 hours to earn $192

c) It represents a mathematical model as it defines a clear relationship between x and y without any probabilistic approach. Means it can be applied again and again without any changes.

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