Question

Judy worked 8 hours and ben worked 10 hours. Their combined pay was $80. When Judy worked 9 hours and ben worked 5 hours. Their combined pay was $65. Find the hourly rate for each person

Answer 1

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Define x and y:
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Let Judy's hourly rate be x.
Let Ben's hourly rate be y.

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Construct Equation:
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8x + 10y = 80 ---------------- (1)
9x + 5y = 65 -----------------(2)

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From Equation (1):
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8x + 10y = 80
4x + 5y = 40 // Divide by 2

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Equation (2) - (1):
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5x = 25
x = 5 //Divide by 5

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Substitute x = 5 into Equation (1):
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4x + 5y = 40
4(5) + 5y = 40 //Sub x = 5
20 + 5y = 40 . //Simplify
5y = 40 - 20 //Subtract 20 from both sides
5y = 20 //Simplfy
y = 4 // Divide by 4

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Find Judy's and Ben's Rate:
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Judy = x = $5/hr
Ben = y = $4/hr

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Ans: Judy's hourly rate is $5 and Ben's hourly rate is $4.
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