Maths question

Let X1, X2 and X3 be the value of the first, second and third prize respectively. Then we have the following:
[1]........ X1+X2+X3=960
[2]........ X2=4/5 * X1
[3]........ X3=3/4 * X2

Substitute [2] into [3], X3 = 3/4 * 4/5 * X1 = 3/5 * X1
Now substitute this and [2] into [1]
X1 + 4/5 * X1 + 3/5 * X1 = 960
or (1+4/5+3/5)*X1 = 960
12/5 * X1 = 960
X1 = 400
Substitute this back into [2] and [3],
X2 = 4/5 * 400 = 320
X3 = 3/4 * 320 = 240

For checking purpose, substitute these values back to the original formulas:
X1+X2+x3 = 400+320+240 = 960 (ok)
X2 = 4/5 * X1 = 4/5 * 400 = 320 (ok)
X3 = 3/4 * X2 = 3/4 * 320 = 240 (ok)

So the value of the three prizes are 400, 320, and 240 respectively.