Question

How to set up a system of equations and solve the word problem: Roy, Sally, and Jeff drive a total of 50 miles to work each day. Sally drives twice as far as Roy, and Jeff drives 10 miles farther than Sally. Find how far each person drives each day.

a) R=10,S=20,J=20

b) R=15,S=30,J=5

c) R=5,S=15,J=30

d) R=20,S=10,J=20

Answer 1

To find the distances Roy, Sally, and Jeff drive each day, set up a system of equations based on the given information, solve for one variable, and then find the others. Roy drives 8 miles, Sally drives 16 miles, and Jeff drives 26 miles each day.

Step-by-step explanation:

To solve this word problem involving distances driven by Roy, Sally, and Jeff, we need to set up a system of equations. We can let R represent the distance Roy drives, S represent the distance Sally drives, and J represent the distance Jeff drives. With the given information, we can express these relationships mathematically:

• Roy's distance: R
• Sally's distance: S = 2R
• Jeff's distance: J = S + 10
• Total distance: R + S + J = 50

Now, substitute S and J in the total distance equation:

R + 2R + (2R + 10) = 50

Simplify the equation to find R:

5R + 10 = 50

Subtract 10 from both sides:

5R = 40

Divide by 5:

R = 8

Now that we have Roy's distance, we can find Sally's and Jeff's:

S = 2 × R = 2 × 8 = 16

J = S + 10 = 16 + 10 = 26

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