Question

On the basis of data from 1990 to​ 2006, the median income y in year x for men and women is approximated by the equations given​ below, where xequals0 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: -255x+2y=56,937Women: - 842x+3y=42,751

Answer 1

In 2083

Explanation:

Given,

The median income y in year x since 1990 for men,

-255x+2y=56,937 .......(1),

For women,

-842x+3y=42,751 ........(2),

From equation (1),

2y = 56937 + 255x

`\implies y = (1)/(2)( 56937 + 255x)`

From equation (2),

842x+3y=42,751,

`3y = 42751 + 842x`

`\implies y =(1)/(3)(42751 + 842x)`

When the median income of men and women are​ same,

`(1)/(2)( 56937 + 255x)=(1)/(3)(42751 + 842x)`

`3( 56937 + 255x)=2(42751 + 842x)`

`170811 + 765x = 85502 + 1684x`

`765x = 85502 + 1684x-170811`

`765x - 1684x = 85502 -170811`

`-919x = -85309`

`\implies x = (85309)/(919)=92.828\approx 93`

∵ 1990 + 93 = 2083,

Hence, in 2083, the median income of men and women would be the​ same