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Ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together, they worked 114 hours. If we denote the number of hours Isaac worked as "x," what equation represents the situation?

A) \( x + x + 6 + 4(6 + x) = 114 \)
B) \( 2x + 6 + 4x = 114 \)
C) \( x + 6 + 4x = 114 \)
D) \( 2x + 4x + 6 = 114 \)

Answer :

Final answer:

To find the number of hours Isaac worked, we use the equation x + (x + 6) + 4(x + 6) = 114. After simplifications, this leads to the equation 6x + 30 = 114, which, when solved, gives x = 14, indicating that Isaac worked for 14 hours.

Explanation:

Let x represent the number of hours Isaac worked. According to the problem, Ruby worked 6 hours more than Isaac, so Ruby worked x + 6 hours. Svetlana worked 4 times as many hours as Ruby, which means she worked 4(x + 6) hours. The total number of hours worked by all three individuals is given as 114 hours.

Therefore, to find the equation that represents the situation, we can add the hours worked by each individual and set it equal to 114:

x + (x + 6) + 4(x + 6) = 114

After simplifying the equation, we have:

x + x + 6 + 4x + 24 = 114

Further simplification gives us the equation that best represents the situation:

x + x + 4x + 6 + 24 = 11

Which simplifies to:

6x + 30 = 114

Subtracting 30 from both sides to solve for x:

6x = 84

Dividing both sides by 6:

x = 14

Therefore, Isaac worked for 14 hours.

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