Allen and Ben are painting a fence. The ratio of the amount of work Allen does to the amount of work Ben does is $3:5$. If the fence requires a total of $240$ square feet to be painted, how many square feet does Ben paint?
Between them, Allen and Ben are dividing the work into $8$ equal parts, $3$ of which Allen does and $5$ of which Ben does. Each part of the work requires $\frac{240}{8} = 30$ square feet to be painted. Since Ben does $5$ parts of the work, he will paint $30 \cdot 5 = \boxed{150}$ square feet of the fence.
150
Level 3
Prealgebra
Problem: Allen and Ben are painting a fence. The ratio of the amount of work Allen does to the amount of work Ben does is $3:5$. If the fence requires a total of $240$ square feet to be painted, how many square feet does Ben paint?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find out how many square feet Ben paints, we first need to understand the ratio of work done by Allen and Ben. The ratio of Allen's work to Ben's work is given as 3:5. This means that for every 3 parts of work Allen does, Ben does 5 parts. 

Next, we can express the total work done in terms of these parts. Let the total parts of work be the sum of the parts done by Allen and Ben. This gives us:

Total parts = 3 (Allen) + 5 (Ben) = 8 parts.

Now, we know the total area of the fence that needs to be painted is 240 square feet. To find the value of one part, we divide the total area by the total number of parts:

1 part = Total area / Total parts = 240 square feet / 8 parts = 30 square feet per part.

Now, we can calculate the amount of work done by Ben. Since Ben does 5 parts of the work, we multiply the number of parts he does by the area represented by one part:

Ben's work = 5 parts * 30 square feet per part = 150 square feet.

Thus, the final answer is 150.<|END_OF_LATENT|> The final answer is $150$.