Elmer has a collection of 300 fossils. Of these, 21% are fossilized snail shells. How many fossilized snail shells does Elmer have?
The Correct Answer and Explanation is:
To find how many fossilized snail shells Elmer has, we are told that 21% of his 300 fossils are snail shells.
Step 1: Understand the meaning of percentage
A percentage is a way of expressing a number as a fraction of 100.
So, 21% means:21%=2110021\% = \frac{21}{100}21%=10021
This tells us that for every 100 fossils, 21 are snail shells.
Step 2: Multiply the percentage by the total number
To find how many snail shells are in a total of 300 fossils, we multiply:21100×300\frac{21}{100} \times 30010021×300=21×300100=6300100=63= \frac{21 \times 300}{100} = \frac{6300}{100} = 63=10021×300=1006300=63
✅ Final Answer:
Elmer has 63 fossilized snail shells.
📘 Textbook-style Explanation (approx. 300 words)
To solve a problem involving percentages, such as determining how many items fall into a certain category based on a percentage, we begin by converting the percentage into a fraction or decimal. In this case, Elmer has a collection of 300 fossils, and 21% of them are fossilized snail shells.
Percent means “per hundred,” so 21% is equal to 21 out of every 100 fossils. To find out how many snail shells that corresponds to in a group of 300 fossils, we use multiplication. We calculate 21% of 300 by multiplying 300 by the decimal form of 21%, which is 0.21. However, we can also solve it more precisely by using fractions:21%=2110021\% = \frac{21}{100}21%=10021Number of fossilized snail shells=21100×300\text{Number of fossilized snail shells} = \frac{21}{100} \times 300Number of fossilized snail shells=10021×300
When multiplying a fraction by a whole number, we multiply the numerator (top part) by the whole number and then divide by the denominator (bottom part):21×300100=6300100=63\frac{21 \times 300}{100} = \frac{6300}{100} = 6310021×300=1006300=63
Therefore, 63 of Elmer’s fossils are fossilized snail shells. This method applies to any percentage problem—multiply the total quantity by the given percent (as a decimal or fraction) to find the part of the whole.
