Roy,Sally, and Jeff drive a total of 50 mi to work each day. Sally drives twice as far as Roy, and Jeff drives 10 miles farther than Sally. Use a system of three equations in three unknowns to find how far each person drives each day.

Let the distances Roy, Sally, and Jeff drive each day be denoted by \( R \), \( S \), and \( J \), respectively. Based on the information provided, we can set up the following system of equations:

1. The total distance driven by all three is 50 miles:
   \[
   R + S + J = 50
   \]
   
2. Sally drives twice as far as Roy:
   \[
   S = 2R
   \]
   
3. Jeff drives 10 miles farther than Sally:
   \[
   J = S + 10
   \]

### Substituting the equations:
1. From equation \( S = 2R \), substitute \( S \) into the equation \( J = S + 10 \):
   \[
   J = 2R + 10
   \]

2. Now substitute both \( S = 2R \) and \( J = 2R + 10 \) into the total distance equation \( R + S + J = 50 \):
   \[
   R + 2R + (2R + 10) = 50
   \]
   
   Simplifying:
   \[
   R + 2R + 2R + 10 = 50
   \]
   \[
   5R + 10 = 50
   \]
   \[
   5R = 40
   \]
   \[
   R = 8
   \]

### Solving for \( S \) and \( J \):
1. \( S = 2R = 2 \times 8 = 16 \)
2. \( J = 2R + 10 = 2 \times 8 + 10 = 26 \)

Thus, Roy drives 8 miles, Sally drives 16 miles, and Jeff drives 26 miles each day.

Would you like further details on the steps or clarifications?

### Related Questions:
1. What if Sally drove three times as far as Roy?
2. How would the solution change if Jeff drove 5 miles farther than Sally instead of 10?
3. Can you solve this problem using a matrix approach?
4. How would you set up the system if they drove a total of 60 miles instead of 50?
5. What if Sally and Roy drove equal distances?

#### Tip: 
For solving systems of equations, substitution is often simpler when one equation is already solved for one variable, as it reduces the number of variables in the remaining equations.

Roy, Sally, and Jeff drive a total of 50 mi to work each day. Sally drives twice as far as Roy, and Jeff drives 10 miles farther than Sally. Use a system of three equations in three unknowns to find how far each person drives each day.

Learn how to solve a system of linear equations to find the distances Roy, Sally, and Jeff drive each day. This problem involves setting up three equations based on total distance and relationships between the drivers' distances. Suitable for students in Grades 8-10.

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