To write the equation for the relationship between hours of work (t) and the paycheck (p), we'll start by using the fact that the pay varies directly with the number of hours worked. This means that we can express the relationship as:
\[ p = kt \]
where \( k \) is the constant of proportionality, which represents the amount of money earned per hour.
Given that for 25 hours of work the paycheck is $312.50, we can substitute these values into the equation to find \( k \):
- Substitute \( p = 312.50 \) and \( t = 25 \) into the equation:
\[ 312.50 = k \cdot 25 \]
- To solve for \( k \), divide both sides by 25:
\[ k = \frac{312.50}{25} = 12.50 \]
So, the constant \( k \) is $12.50, which means the person earns $12.50 per hour.
- Now that we have the value of \( k \), we can write the final equation for the relationship between hours of work and pay:
\[ p = 12.50t \]
Explanation:
- The equation \( p = 12.50t \) represents the direct variation between the paycheck (\( p \)) and the hours worked (\( t \)).
- The constant \( k \) indicates that for every hour worked, the person earns $12.50, and that is how we derived our equation using the information provided about their earnings for 25 hours of work.
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