A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Let $x$ be the number of paperclips that a box with a volume of 48 $\text{cm}^3$ could hold. Setting up the ratio $\frac{50}{16}=\frac{x}{48}$ and solving for $x$ gives $x=150$.  Hence, a 48 $\text{cm}^3$ box could hold $\boxed{150}$ paperclips.  We also could have noted that tripling the size of the box triples the number of paperclips we can hold, so the new box can hold $50\cdot 3 = 150$ paperclips.
150
Level 1
Algebra
Problem: A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine how many paperclips a box with a volume of 48 cm³ can hold, we first need to establish the relationship between the volume of the box and the number of paperclips it can accommodate. 

Given that a box with a volume of 16 cm³ holds 50 paperclips, we can calculate the volume occupied by each paperclip. This is done by dividing the volume of the box by the number of paperclips it holds:

Volume per paperclip = 16 cm³ / 50 paperclips = 0.32 cm³ per paperclip.

Next, we apply this volume per paperclip to the larger box with a volume of 48 cm³. To find out how many paperclips can fit in this box, we divide the total volume of the box by the volume occupied by each paperclip:

Number of paperclips = 48 cm³ / 0.32 cm³ per paperclip.

Calculating this gives:

Number of paperclips = 48 / 0.32 = 150.

Thus, a box with a volume of 48 cm³ can hold 150 paperclips.<|END_OF_LATENT|> The final answer is $150$.