Two welders worked a total of 47 h on a project. One welder made $37/h,...

Connor Randall

Connor Randall

Answered

2022-01-20

Two welders worked a total of 47 h on a project. One welder made $37/h, while the other made $39/h. If the gross earnings of the two welders was $1781 for the job, how many hours did each welder work? Using row- echron matrix.

Answer & Explanation

Deegan Mullen

Deegan Mullen

Expert

2022-01-21Added 12 answers

Step 1
Solving a system of equations using row-echlon form can be done by reducing the given matrix to another matrix, using transformations, such that each entry below the diagonal element of each column is 0.
Step 2
Let the two welders work for x and y hours respectively. As the total hours for which the two welders work is 47, hence we will have:
x+y=47 (i)
Also, the welders earn at a rate of 37 h and 39 h respectively and their gross earning was $1781. Hence we will have:
37x+39y=1781 (ii)
Thus we have a system of two linear equations which can be transformed to the matrix form as shown below:
[113738](xy)=[471781]
We can solve this system of equations by transforming it into a row-echlon form as shown below:
[113739](xy)=[471781]
R2R237R1
[1102](xy)=[4742]
Note: Here we already obtain the row−echlon form and can use it to find the required values of x and y, but we go a step further and completelpy convert the matrix into an identity matrix to directly obtain the required values.
R212R2
[1101](xy)=[4721]
R1R1R2
[1001](xy)=[2621]
Thus we get the solution as, x=26 and y=21. Hence, the welders work for 26 hrs and 21 hrs respectively.

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