Question
Marcus and Layla share pencils in a ratio of 3:2. They have 25 pencils total. How many pencils does Marcus have?
Answers
Answered by
GPT-4o mini
To find out how many pencils Marcus has, we start with the given ratio of pencils between Marcus and Layla, which is 3:2. This means for every 3 pencils Marcus has, Layla has 2 pencils.
First, let's determine the total number of parts in the ratio:
\[
3 + 2 = 5 \text{ parts}
\]
Next, we can calculate the value of one part by dividing the total number of pencils (25) by the total number of parts (5):
\[
\text{Value of one part} = \frac{25}{5} = 5
\]
Now, we can determine how many pencils Marcus has by multiplying the number of parts he receives (3 parts) by the value of one part:
\[
\text{Pencils Marcus has} = 3 \times 5 = 15
\]
Thus, Marcus has 15 pencils.
To confirm, we can also calculate how many pencils Layla has:
\[
\text{Pencils Layla has} = 2 \times 5 = 10
\]
Adding both quantities gives:
\[
15 + 10 = 25 \text{ pencils (total)}
\]
The calculations are correct. Therefore, Marcus has \(\boxed{15}\) pencils.
First, let's determine the total number of parts in the ratio:
\[
3 + 2 = 5 \text{ parts}
\]
Next, we can calculate the value of one part by dividing the total number of pencils (25) by the total number of parts (5):
\[
\text{Value of one part} = \frac{25}{5} = 5
\]
Now, we can determine how many pencils Marcus has by multiplying the number of parts he receives (3 parts) by the value of one part:
\[
\text{Pencils Marcus has} = 3 \times 5 = 15
\]
Thus, Marcus has 15 pencils.
To confirm, we can also calculate how many pencils Layla has:
\[
\text{Pencils Layla has} = 2 \times 5 = 10
\]
Adding both quantities gives:
\[
15 + 10 = 25 \text{ pencils (total)}
\]
The calculations are correct. Therefore, Marcus has \(\boxed{15}\) pencils.