First we invent some variables which we hope to reduce as we start to solve the problem. Let m, b, n, d represent the investment amounts for the money market account, the bond fund, the international and domestic stock funds respectively.
Now we can apply the given facts:
m+b+n+d=$100000 (total investment);
m+b=$60000 (60% of $100000);
d=4n, and since n+d=$40000 (40% of $100000), 5n=$40000, n=$8000 and d=$32000.
We also know that after a year the total interest is $4000, so:
0.025m+0.035b+0.04n+0.06d=$4000 (annual return).
We plug in n=8000 and d=32000:
0.025m+0.035b+320+1920=4000;
0.025m+0.035b=4000-2240=1760.
b=60000-m so we substitute for b:
0.025m+0.035(60000-m)=1760.
We can solve this for m:
0.025m+2100-0.035m=1760;
2100-1760=0.01m;
340=0.01m, m=$34000 and b=60000-34000=$26000.
So $34,000, $26,000, $8,000 and $32,000 should be invested in the money market, bond fund, international and domestic stock funds respectively.