Question

Need help with mixture problems with system of linear please see attached picture

Answer 1

The Solution:

Let the first mechanic rate per hour be x and the second mechanic rate per hour be y.

Representing the given problem in equations, we have:

$\begin{gathered} 20x+5y=1800\ldots\text{eqn}(1) \\ x+y=165\ldots\text{eqn}(2) \end{gathered}$

We are asked to find the values of x and y.

Step 1:

From eqn(2), find y.

$y=165-x\ldots\text{eqn}(3)$

Step 2:

putting eqn(3) into eqn(1), we get

$20x+5(165-x)=1800$

Simplifying, we get

$20x+825-5x=1800_{}$

Collecting the like terms, we get

$\begin{gathered} 20x-5x=1800-825 \\ 15x=975 \end{gathered}$

Dividing both sides by 15, we get

$x=\frac{975}{15}=65=\text{ \ 65}$

Step 3:

Substituting 65 for x in eqn(3), we get

$\begin{gathered} y=165-65 \\ y=100=\text{ \ 100} \end{gathered}$

Therefore, the correct answers are:

The first mechanic charges $65 per hour.

The second mechanic charges $100 per hour.