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Ben works as a park ranger and makes $35 an hour.

His friend Steve works at a nature tour guide and makes $30 an hour and an additional $20 in tips per day.
1) Write an equation that represents Ben's wage. Let x represent the number of hours he works and y represent how much he earns.
2) Write an equation that represents Steve's wage. Let x represent the number of hours he works and y represent how much he earns.
4) The solution of the system of equations means that when they both work
hours, they both make $

1 answer

  1. Ben's wage can be represented by the equation:
    \[ y = 35x \]
    Where \( y \) is the total earnings and \( x \) is the number of hours Ben works.

  2. Steve's wage can be represented by the equation:
    \[ y = 30x + 20 \]
    Where \( y \) is the total earnings, \( x \) is the number of hours Steve works, and \( 20 \) represents the tips he earns per day.

  3. To find the solution of the system of equations, we need to set both equations equal to each other since we're looking for when they make the same amount of money (y).

So we set:

\[ 35x = 30x + 20 \]

Now, solving for \( x \):

  1. Subtract \( 30x \) from both sides: \[ 35x - 30x = 20 \] \[ 5x = 20 \]

  2. Divide both sides by 5: \[ x = 4 \]

Now, substitute \( x = 4 \) back into either equation to find \( y \):

Using Ben's equation: \[ y = 35(4) = 140 \]

We can also check using Steve's equation: \[ y = 30(4) + 20 = 120 + 20 = 140 \]

Thus, the solution of the system of equations means that when they both work 4 hours, they both make $140.