Question

Mrs. Chen bought a big tub of 250 plastic geometric pieces to use in her math classes. The pieces are all a similar size but different shapes. She randomly selects a handful of pieces from the tub. The table below shows the geometric shapes she selects.

Geometric shape Number selected
triangle 3
square 2
hexagon 2
pentagon 4
rectangle 2
Based on the data, estimate how many pentagons are in the tub.
If necessary, round your answer to the nearest whole number.

Answer 1

To estimate the number of pentagons in the tub, we can use the proportion of pentagons in the sample of geometric shapes that Mrs. Chen selected and apply it to the total number of geometric shapes in the tub.

The proportion of pentagons in the sample is:

4 / (3 + 2 + 2 + 4 + 2) = 4 / 13 ≈ 0.31

We can assume that this proportion is representative of the entire tub of geometric shapes, and we can apply it to the total number of geometric shapes in the tub:

0.31 x 250 ≈ 77.5

Rounding to the nearest whole number, we can estimate that there are approximately 78 pentagons in the tub.

Therefore, the estimated number of pentagons in the tub is 78.