Answer:
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
