Respuesta :
Answer:
Austin's hourly wage is $8.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
Tara's hourly wage is x.
Kayte's hourly wage is y.
Austin's hourly wage is z.
Tara earns twice as much per hour as Kayte.
This means that [tex]x = 2y[/tex]
Kayte earns $3 more per hour than Austin.
This means that [tex]y = z + 3[/tex]
As a group, they earn $41 per hour.
This means that [tex]x + y + z = 41[/tex]
What is Austin's hourly wage?
This is z.
[tex]x + y + z = 41[/tex]
[tex]y = z + 3[/tex] and [tex]x = 2y[/tex], so [tex]x = 2(z + 3) = 2z + 6[/tex]
[tex]x + y + z = 41[/tex]
[tex]2z + 6 + z + 3 + z = 41[/tex]
[tex]4z + 9 = 41[/tex]
[tex]4z = 32[/tex]
[tex]z = \frac{32}{4}[/tex]
[tex]z = 8[/tex]
Austin's hourly wage is $8.
Answer:
Austin's hourly wage is $8.
Step-by-step explanation:
We can write this problem as a system of linear equations.
We define T: Tara's hourly wage, A: Austin's hourly wage and K: Kayte's hourly wage.
Then, if Tara earns twice as much per hour as Kayte, we have:
[tex]T=2K[/tex]
If Kayte earns $3 more per hour than Austin, we have:
[tex]K=A+3[/tex]
And if they earn $41 per hour as a group, we know:
[tex]T+K+A=41[/tex]
We can use all equations to replace in the third one, as:
[tex]T+K+A=41\\\\(2K)+K+A=41\\\\3K+A=41\\\\3(A+3)+A=41\\\\3A+9+A=41\\\\4A=41-9=32\\\\A=32/4=8[/tex]
Austin's hourly wage is $8.
