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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 :

Answer:

In 2083

Step-by-step 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

[tex]\implies y = \frac{1}{2}( 56937 + 255x)[/tex]

From equation (2),

842x+3y=42,751,

[tex]3y = 42751 + 842x[/tex]

[tex]\implies y =\frac{1}{3}(42751 + 842x)[/tex]

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

[tex]\frac{1}{2}( 56937 + 255x)=\frac{1}{3}(42751 + 842x)[/tex]

[tex]3( 56937 + 255x)=2(42751 + 842x)[/tex]

[tex]170811 + 765x = 85502 + 1684x[/tex]

[tex]765x = 85502 + 1684x-170811[/tex]

[tex]765x - 1684x = 85502 -170811[/tex]

[tex]-919x = -85309[/tex]

[tex]\implies x = \frac{85309}{919}=92.828\approx 93[/tex]

∵ 1990 + 93 = 2083,

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

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