Ali and jake went on a cross country trip they took a train part of the way and took a bus the rest of the way they traveled a total of 1450 riding on the train 150 more kilometers than on the bus
let x=kilometers traveled by bus
let y = kilometers traveled by train
question how many kilometers did they travel by train?

They traveled 800 km by train.

Step-by-step explanation:

We assign variables and write two equations. Then we solve the system of 2 equations in 2 unknowns.

Assign variables:

let x = kilometers traveled by bus

let y = kilometers traveled by train

Write first equation:

"they traveled a total of 1450 km"

x + y = 1450

Write second equation:

"riding on the train 150 more kilometers than on the bus"

The distance on the train, y, is 150 km greater than the distance on the bus, x.

y = x + 150

We have a system of 2 equations:

x + y = 1450

y = x + 150

Since the second equation is already solved for y, we can use the substitution method. Substitute y of the first equation with x + 150.

x + y = 1450

x + x + 150 = 1450

2x + 150 = 1450

2x = 1300

x = 650

y = x + 150

y = 650 + 150

y = 800

They traveled 800 km by train.