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

Question

His friend Steve works at a nature tour guide and makes $30 an hour and an additional $20 in tips per day.



(1 point)
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.

3) Graph this system of equations into Desmos. Click here to open Desmos.

4) The solution of the system of equations means that when they both work
hours, they both make $
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Answer 1

1. To represent Ben's wage, we can write the following equation:

\[ y = 35x \]

where \( y \) is the total amount Ben earns, and \( x \) is the number of hours he works.

2. To represent Steve's wage, we can write the following equation:

\[ y = 30x + 20 \]

where \( y \) is the total amount Steve earns, \( x \) is the number of hours he works, and the term \( +20 \) represents the tips he earns per day.

3. To graph these equations in Desmos, you can enter the equations \( y = 35x \) and \( y = 30x + 20 \) into the graphing calculator.

4. The solution of the system of equations means that when they both work the same number of hours, they both make the same amount of money \( y \). You can find this by setting the two equations equal to each other and solving for \( x \):

\[ 35x = 30x + 20 \]

Subtracting \( 30x \) from both sides gives:

\[ 5x = 20 \]

Dividing by 5 gives:

\[ x = 4 \]

To find out how much they both make when they work 4 hours, we can substitute \( x = 4 \) back into either equation:

For Ben:

\[ y = 35(4) = 140 \]

For Steve:

\[ y = 30(4) + 20 = 120 + 20 = 140 \]

So, when they both work 4 hours, they both make $140.