Great job! Now that we have performed the operations on both sides, let's continue the equation from where we left off:
Starting from: \[ 50 + 5x = 60 - 50 \]
Now, subtract \(50\) from \(60\): \[ 50 + 5x = 10 \]
Next, we want to isolate the term with \(x\). To do that, we subtract \(50\) from both sides: \[ 50 + 5x - 50 = 10 - 50 \]
This simplifies to: \[ 5x = -40 \]
Now, we'll divide both sides by \(5\) to solve for \(x\): \[ x = \frac{-40}{5} \] \[ x = -8 \]
This shows that the initial algebra was incorrect. Let’s retrace our steps to ensure we find when Ballio and Mary Beth bike the same number of miles properly.
- Start from: \[ 50 + 15x = 60 + 10x \]
- Subtract \(10x\) from both sides: \[ 50 + 15x - 10x = 60 \] This simplifies to: \[ 50 + 5x = 60 \]
- Next, subtract \(50\) from both sides: \[ 5x = 10 \]
- Finally, divide both sides by \(5\): \[ x = 2 \]
So, the number of weeks until Ballio and Mary Beth have the same number of miles biked each week is \(x = 2\). Now to find how many miles they bike at that time, we can substitute \(x = 2\) into either equation.
For Ballio: \[ y = 50 + 15(2) = 50 + 30 = 80 \]
For Mary Beth: \[ y = 60 + 10(2) = 60 + 20 = 80 \]
Both bikers reach the same mileage of \(80\) miles after \(2\) weeks.
Thus, the point of intersection is: \[ (2, 80) \]
Congratulations on finding the point of intersection!
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