Mr. and mrs. patton and their daughter carolyn own three cars. carolyn drives 10 miles per week farther with her car than her father does with his. mr. patton does twice as many miles per week as mrs. patton. if their total mileage per week is 160 miles, how many miles per week does each drive?

X = mr. pattons miles, y = mrs. patton's miles, z = carolyn's miles

x + y + z = 160
z = x + 10 z = 2y + 10
x = 2y

2y + y + 2y + 10 = 160
5y + 10 = 160
5y = 160 - 10
5y = 150
y = 150/5
y = 30 <=== mrs. patton drives 30 miles

x = 2y
x = 2(30)
x = 60mr. patton drives 60 miles

z = x + 10
z = 60 + 10
z = 70 <== carolyn drives 70 miles