Question

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 drives twice as many miles per week as Mrs. Patton. If their total mileage per week is 160 miles, how many miles per does each drive?

Answer 1

Answer:

Mr. Patton: 60 miles;

Mrs. Patton: 30 miles,

Carolyn: 70 miles.

Step-by-step explanation:

Let x, y and z be number of miles driven by Carolyn, Mr. Patton and Mrs. Patton respectively.

We have been given that 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. We can represent this information in an equation as: $x=y+10...(1)$.

Mr. Patton drives twice as many miles per week as Mrs. Patton. We can represent this information in an equation as: $y=2z...(2)$.

Their total mileage per week is 160 miles. We can represent this information in an equation as: $x+y+z=160...(3)$.

Substituting equation (1) and (2) in equation (3), we will get:

$y+10+y+\frac{y}{2}=160$

$y+10-10+y+\frac{y}{2}=160-10$

$2y+\frac{y}{2}=150$

$\frac{2*2y}{2}+\frac{y}{2}=150$

$\frac{4y}{2}+\frac{y}{2}=150$

$\frac{5y}{2}=150$

$\frac{5y}{2}*2=150*2$

$y=30*2$

$y=60$

Therefore, Mr. Patton drove 60 miles.

$y=2z$

$60=2z$

$\frac{60}{2}=\frac{2z}{2}$

$30=z$

Therefore, Mrs. Patton drove 30 miles.

$x=y+10$

$x=60+10$

$x=70$

Therefore, Carolyn drove 70 miles.

Answer 2

Let's say Mr. Patton = x, Mrs. Patton = y, and Carolyn = z
Now just rewrite it as an equation with the given information.
x + y + z = 160
z = x + 10
x = 2y
Mr. Patton would drive 60 miles, Mrs. Patton would drive 30, and Carolyn would drive 70.