I made an error in my post regarding the second interpretation...here's what I should have posted:

I interpreted the 3:4 ratio as pertaining to Mark's shortfall they helped cover. If we interpret it as you suggest, then:

The amount that Mark was short was 1/8 of the cost of the present (1/2 of his 1/4 share). Steve and Jason covered this shortfall. Let k be the portion Steve covered and so 1 - k would be the portion Jason covered. And so we could write:

\(\displaystyle \frac{\frac{1}{4}+k\frac{1}{8}}{\frac{1}{4}+(1-k)\frac{1}{8}}=\frac{3}{4}\)

\(\displaystyle 1+\frac{1}{2}k=\frac{3}{4}+\frac{3}{8}(1-k)\)

\(\displaystyle 8+4k=6+3(1-k)\)

\(\displaystyle 8+4k=6+3-3k\)

\(\displaystyle 7k=1\)

\(\displaystyle k=\frac{1}{7}\)

Hence, letting \(P\) be the cost of the present:

\(\displaystyle P\left(\left(1-\frac{1}{7}\right)\frac{1}{8}\right)=24\)

\(\displaystyle P\left(\frac{6}{7}\cdot\frac{1}{8}\right)=24\)

\(\displaystyle P\left(\frac{3}{28}\right)=24\)

\(\displaystyle P=24\cdot\frac{28}{3}=224\quad\checkmark\)

Sorry for the confusion.