Question

On the basis data from 1990 to 2006, the median income y in the year x for men and women is approximated by the equation given below, where x=0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future in what year will the median income of men and women be the same?

Men: -245x+2y=58,990

Women: -847x+3y=48,484

Answer 1

Given Equations

Men: -245x+2y=58,990

Women: -847x+3y=48,484

Rearrange the equations in terms of median income (y)

2y = 58990 + 245x ...................(1)

3y = 48484 + 847x ...................(2)

simplifying equations we get

$y = \frac{58990}{2}$ + $\frac{245}{2}$

$y = 29495 + \frac{245x}{2}$ ....................(3)

$y = \frac{48484}{3} + \frac{847x}{3}$..................(4)

Equating Equations (3) and (4)

$29495 + \frac{245x}{2} = \frac{48484}{3} + \frac{847x}{3}$

$29495 - \frac{48484}{3} = \frac{847x}{3} - \frac{245x}{2}$

$\frac{40001}{3} = \frac{1694x - 735x}{6}$

$\frac{40001}{3} = \frac{959x}{6}$

$40001 = \frac{959x}{2}$

40001 * 2 = 959x

80002 = 959x

$x = \frac{80002}{959}$

x = 83.4 ~ 83 years

x=0 corresponds to 1990

So after 83 years that is 1990 + 83 = 2073

Hence the median income = 2073