Carl and Derrick are part-time employees. They are paid different hourly rates. One week, Carl worked for 15 hours and Derrick worked for 20 hours. Their combined pay was $640. The next week, Carl worked 20 hours and Derrick worked 25 hours. Their combined pay was $820. What is Carl's hourly pay rate?

Carl's hourly pay rate is $16

Step-by-step explanation:

Let x is the hourly rate of Carl and y is the hourly rate of Derrick

∵ Carl's hourly rate is $x

∵ Derrick's hourly rate is $y

∵ Carl worked for 15 hours and Derrick worked for 20 hours

∴ Their combined pay was 15x + 20y

∵ Their combined pay was $640

→ Equate the value of the combined pay

∴ 15x + 20y = 640 ⇒ (1)

∵ The next week, Carl worked 20 hours and Derrick worked 25 hours

∴ Their combined pay was 20x + 25 y

∵ Their combined pay was $820

→ Equate the value of the combined pay

∴ 20x + 25y = 820 ⇒ (2)

Now we have a system of equations to solve it

→ Multiply equation (1) by 5 and equation (2) by -4

∵ 5(15x) + 5(20y) = 5(640)

∴ 75x + 100y = 3200 ⇒ (3)

∵ -4(20x) + -4(25y) = -4(820)

∴ -80x - 100y = -3280 ⇒ (4)

→ Add equations (3) and (4)

∵ (75x + -80x) + (100y + -100y) = (3200 + -3280)

∴ -5x + 0 = -80

∴ -5x = -80

→ Divide both sides by -5 to find x

∴ x = 16

∴ Carl's hourly pay rate is $16

6 (3) - 4 + 32

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