Problem Solving

Taniuca wrote:a number line, a < b < c < d. The distance from a to b is of the distance from b to d. The distance from a to c is 3 times the distance from c to d. What is the value of ?

I think the correct problem read like this:

On a number line, a<b<c<d. The distance from a to b is 1/4 of the distance from b to d. The distance from a to c is 3 times the distance from c to d. What is the value of (b-a)/(c-a)?

Choose the values of a, b, c and d conveniently but in accordance with the given constraints.

Set a = 0 and b = 1
As the distance from a to b is 1/4 of the distance from b to d
=> (b - a) = (d - b)/4
=> (1 - 0) = (d - 1)/4
=> d = 4 + 1 = 5

As the distance from a to c is 3 times the distance from c to d
=> (c - a) = 3(d - c)
=> (c - 0) = 3(5 - c)
=> c + 3c = 15
=> c = 15/4

Thus, (b - a)/(c - a) = b/c = 4/15

The correct answer is C.