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Arla and kal both work in jobs they get paid by the hour in their first week on the job they each worked 40 hours and together there total earnings were $1300 in their second week on the job business was slow so arla worked 20 hours and kal worked 16 hours their total pool earning was $580 what is each persons hourly wage

Respuesta :

frika

Answer:

Arla - $15, Kal - $17.5

Step-by-step explanation:

Let $x be Arla's hourly wage and $y be Kal's hourly wage.

1. In the first week on the job they each worked 40 hours and earned $(40x+40y) together. Their total earnings were $1300, so

40x+40y=1300.

2. In the second week on the job business was slow so Arla worked 20 hours and earned $20x, Kal worked 16 hours and earned $16y, $(20x+16y) in total. Their total pool earning was $580, so

20x+16y=580.

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}40x+40y=1300\\20x+16y=580\end{array}\right.\Rightarrow \left\{\begin{array}{l}40x+40y=1300\\40x+32y=1160\end{array}\right..[/tex]

Subtract them:

[tex]40y-32y=1300-1160,\\ \\8y=140,\\ \\y=\$17.5.[/tex]

Then

[tex]40x+40\cdot 17.5=1300,\\ \\40x=1300-700,\\ \\40x=600,\\ \\x=\$15.[/tex]

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