Question

there are fifteen workers employed on a highway project, some at $180 per day and some at $155 per day. The daily payroll is $2400. Let x represent the number of $180 per day workers and let y represent the number of $155 per day workers. Write and solve a linear system to find the number of workers employed at each wage.​

Answer 1

there are 3 workers who earn $180 per day and 12 workers who earn $155 per day

Explanation:

Let x be the number of workers who earn $180 per day and y be the number of workers who earn $155 per day.

From the problem statement, we know that:

The total number of workers is 15. Therefore, x + y = 15.

The total daily payroll is $2400. Therefore, 180x + 155y = 2400.

We now have a system of two linear equations with two variables:

x + y = 15

180x + 155y = 2400

We can solve this system by substitution or elimination. Here, we will use the substitution method.

From the first equation, we know that y = 15 - x. We can substitute this expression for y in the second equation:

180x + 155(15 - x) = 2400

Simplifying and solving for x, we get:

180x + 2325 - 155x = 2400

25x = 75

x = 3

We can now use this value of x to find y:

y = 15 - x = 15 - 3 = 12

Therefore, there are 3 workers who earn $180 per day and 12 workers who earn $155 per day.