Question

) Tara earns twice as much per hour as Kayte.

Kayte earns $3 more per hour than Austin. As
a group, they earn $41 per hour. What is
Austin's hourly wage?​

Answer 1

Austin's hourly wage is $8.

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:

`T=2K`

If Kayte earns $3 more per hour than Austin, we have:

`K=A+3`

And if they earn $41 per hour as a group, we know:

`T+K+A=41`

We can use all equations to replace in the third one, as:

`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`

Austin's hourly wage is $8.

Answer 2

Austin's hourly wage is $8.

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
`x = 2y`

Kayte earns $3 more per hour than Austin.

This means that
`y = z + 3`

As a group, they earn $41 per hour.

This means that
`x + y + z = 41`

What is Austin's hourly wage?​

This is z.

`x + y + z = 41`

`y = z + 3` and
`x = 2y`, so
`x = 2(z + 3) = 2z + 6`

`x + y + z = 41`

`2z + 6 + z + 3 + z = 41`

`4z + 9 = 41`

`4z = 32`

`z = (32)/(4)`

`z = 8`

Austin's hourly wage is $8.