Question 12408
Let D = day time rate and E = evening rate.

{{{20(D) + 20(E) = 280}}} and
{{{30(D) + 12(E) = 276}}} Multiply the 1st equation by 3 and the 2nd equation by 2.

{{{60D + 60E = 840}}} and
{{{60D + 24E = 552}}} Now subtract the 2nd equation from the 1st equation.

{{{36E = 288}}} Divide both sides by 36.
{{{E = 8}}} Substitute this into 2nd equation and solve for D.

{{{20D + 20(8) = 280}}}
{{{20D + 160 = 280}}} Subtract 160 from both sides.
{{{20D = 120}}} Divide both sides by 20.
{{{D = 6}}}

Daytime rate is $6.00 per hour.
Evening rate is $8.00 per hour.