A and D that’s the answer
This is an exponential equation. We will solve in the following way. I do not have special symbols, functions and factors, so I work in this way
2 on (2x) - 5 2 on x + 4=0 =>. (2 on x)2 - 5 2 on x + 4=0 We will replace expression ( 2 on x) with variable t => 2 on x=t =. t2-5t+4=0 => This is quadratic equation and I solve this in the folowing way => t2-4t-t+4=0 => t(t-4) - (t-4)=0 => (t-4) (t-1)=0 => we conclude t-4=0 or t-1=0 => t'=4 and t"=1 now we will return t' => 2 on x' = 4 => 2 on x' = 2 on 2 => x'=2 we do the same with t" => 2 on x" = 1 => 2 on x' = 2 on 0 => x" = 0 ( we know that every number on 0 gives 1). Check 1: 2 on (2*2)-5*2 on 2 +4=0 => 2 on 4 - 5 * 4+4=0 => 16-20+4=0 =. 0=0 Identity proving solution.
Check 2: 2 on (2*0) - 5* 2 on 0 + 4=0 => 2 on 0 - 5 * 1 + 4=0 =>
1-5+4=0 => 0=0 Identity provin solution.
I am setting the week hourly rate to x, and the weekend to y. Here is how the equation is set up:
13x + 14y = $250.90
15x + 8y = $204.70
This is a system of equations, and we can solve it by multiplying the top equation by 4, and the bottom equation by -7. Now it equals:
52x + 56y = $1003.60
-105x - 56y = -$1432.90
Now we add these two equations together to get:
-53x = -$429.30 --> 53x = $429.30 --> (divide both sides by 53) x = 8.10. This is how much she makes per hour on a week day.
Now we can plug in our answer for x to find y. I am going to use the first equation, but you could use either.
$105.30 + 14y = $250.90. Subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40
Now we know that she makes $8.10 per hour on the week days, and $10.40 per hour on the weekends. Subtracting 8.1 from 10.4, we figure out that she makes $2.30 more per hour on the weekends than week days.
