Physics 1111 Question Internal Explosion

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 2.2 times the mass of the other.

If 7900 J were released in the explosion, how much kinetic energy did each piece acquire?
Express your answers using two significant figures.

I got 5500 and 2400, which makes sense, but 2400 is wrong/very close. What did i do wrong?

Here's how I'd do it:

What you can assume is that momentum is conserved, so m1*v1 = m2*v2, which means that the heavy piece has half the speed of the other piece. If the small piece has mass m and speed v, the large piece has mass 2m and speed v/2, and it has kinetic energy (1/2) * (2m) * (v/2)^2 = (1/2)mv^2 * 2/2^2 = (1/2)mv^2 * (1/2)

The heavier piece has half the KE of the larger piece. If they add up to 7900, then the light piece has (2/3) of 7900 J and the heavy piece has (1/3) of 7900 J.

Edit: Sorry, I read that as 2.0, not 2.2. Hang on a minute.

Corrections:
v2 = v/2.2
KE2 = (1/2)mv^2 * 2.2/(2.2)^2 = KE1 / 2.2

So KE1 + KE2 = (1 + 1/2.2)KE1 = 7900 = 1.45 * KE1
KE1 = 7900/1.45 = 5450 J
KE2 = 5450J/2.2 = 2480 J
or to 2 significant figures, 5400 and 2500.