An Australian study found that, if other factors are constant (education, experience, etc.), taller people receive higher wages for the same work. The study reported a “height premium” for men of 3% of the hourly wage for a 10 cm increase in height; for women the height premium reported was 2%. We assume that hourly wages are a linear function of height. The slope is given by the height premium at the average hourly wage for that gender, AU$29.40 for men and AU$24.78 for women.

(a) The average hourly wage for a 178 cm Australian man is AU$29.40. Express the average hourly wage of an Australian man as a function of his height, x cm. 

(b) The average hourly wage for a 164 cm Australian woman is AU$24.78. Express the average hourly wage of an Australian woman as a function of her height, y cm. 

(c) What is the difference in average hourly wages between men and women of height 178 cm? 

(d) Is there a height for which men and women are predicted to have the same wage? If so, what is it?