At a tech seminar, the ratio of the number of software engineers present to the number of UI designers present is 5:3. If no software engineer is absent and the number of UI designers who are absent is 24, which accounts for 30% of the total number of registered attendees, how many software engineers are registered for the seminar?

The correct answer is 35.

Step 1: Calculate the total number of registered attendees.
We are given that 24 UI designers are absent, and this number accounts for 30% of the total registered attendees.
Let $T$ be the total number of registered attendees.
$30\%\times T=24$
$0.30\times T=24$
$T=\frac{24}{0.30}=80$
Thus, the total number of registered attendees is 80.

Step 2: Define registered and present attendees.
Let $S_{\text{reg}}$ be the number of registered software engineers.
Let $D_{\text{reg}}$ be the number of registered UI designers.
Since no software engineer is absent, all registered software engineers are present:
$S_{\text{present}}=S_{\text{reg}}$
Since 24 UI designers are absent, the number of present UI designers is:
$D_{\text{present}}=D_{\text{reg}}-24$

Step 3: Form an equation combining total attendees and present UI designers.
The total registered attendees is the sum of registered software engineers and registered UI designers:
$S_{\text{reg}}+D_{\text{reg}}=80$
Substitute $D_{\text{reg}}=D_{\text{present}}+24$ into the equation:
$S_{\text{reg}}+D_{\text{present}}+24=80$
$S_{\text{reg}}+D_{\text{present}}=56$

Step 4: Use the ratio of present attendees to solve for registered software engineers.
The ratio of present software engineers to present UI designers is 5:3:
$\frac{S_{\text{present}}}{D_{\text{present}}}=\frac{5}{3}$
Since $S_{\text{present}}=S_{\text{reg}}$, we have:
$D_{\text{present}}=\frac{3}{5}{S}_{\text{reg}}$
Substitute this into $S_{\text{reg}}+D_{\text{present}}=56$:
$S_{\text{reg}}+\frac{3}{5}{S}_{\text{reg}}=56$
$\frac{8}{5}{S}_{\text{reg}}=56$
$S_{\text{reg}}=56\times \frac{5}{8}$
$S_{\text{reg}}=7\times 5=35$

Therefore, the total number of registered software engineers is 35.