SOLUTION: a student was walking to school. after going 1 kilometer and half of the rest of the trip, there was still 1 kilometer more than a third of the whole left. how far was the student

Question 965193: a student was walking to school. after going 1 kilometer and half of the rest of the trip, there was still 1 kilometer more than a third of the whole left. how far was the student living from the school?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the length of the trip.

he traveled 1 kilometer and half of the rest of the trip.

this is equal to 1 + 1/2 * (x-1).

there was still 1 kilometer more than a third of the whole left.

this is equal to 1 + 1/3 * x

the length of the trip is equal to the length traveled plus the length left to be traveled.

x is the length of the trip.
the length traveled is equal to 1 + 1/2 * (x-1)
the length left to be traveled is equal to 1 + 1/3 * x

your equation is:

x = 1 + 1/2 * (x-1) + 1 + 1/3 * x

simplify to get:

x = 1 + 1/2 * x - 1/2 + 1 + 1/3 * x

group like terms to get:

x = (1 - 1/2 + 1) + (1/2 * x + 1/3 * x)

convert to common denominators to get:

x = (2/2 - 1/2 + 2/2) + (3/6 * x + 2/6 * x)

finish combining like terms to get:

x = 3/2 + 5/6 * x

subtract 5/6 * x from both sides of the equation to get:

x - 5/6 * x = 3/2

convert to common denominators to get:

6/6 * x - 5/6 * x = 3/2

combine like terms to get:

1/6 * x = 3/2

multiply both sides of this equation by (6/1) to get:

x = 18/2 which simplifies to x = 9.

that's your solution.

let's see if it's good.

the whole trip is 9 kilometers.

he traveled 1 kilometer plus half of the rest which means he traveled 1 kilometer plus 1/2 * 8 = 1 + 4 = 5 kilometers.

what remained to be traveled was 1 + 1/3 * the whole trip which means what remained to be traveled = 1 + 1/3 * 9 = 1 + 3 = 4 kilometers.

he traveled 5 kilometers.
he had 4 kilometers left to be traveled.

5 + 4 = 9 which is equal to the whole trip.

solution looks good.

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