Question

Adam has bought a certain number of apples. Jen has bought 5 times the fruit that Adam has bought. If Jen has bought two and a half dozen apples how many apples does Adam have?

• A. 6 apples
• B. 8 apples
• C. 12 apples
• D. 24 apples
• E. 30 apples

Hint:

Break down word problems into smaller pieces of information. First, identify the known quantities (like "a dozen"), then define variables for the unknowns, and finally, translate the relationships into mathematical equations.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a word problem that can be solved by setting up a simple equation based on the given information.
Step 2: Key Formula or Approach:
First, convert the quantity "two and a half dozen" into a specific number.
- 1 dozen = 12 items.
Then, set up an equation relating the number of apples Adam has to the number of apples Jen has.
Step 3: Detailed Explanation:
Let A be the number of apples Adam has.
Let J be the number of apples Jen has.
From the problem, "Jen has bought 5 times the fruit that Adam has bought":
\[ J = 5 \times A \] We are also told that "Jen has bought two and a half dozen apples". Let's calculate this number:
\[ \text{Two and a half dozen} = 2.5 \times 12 \] \[ 2.5 \times 12 = 30 \] So, Jen has 30 apples (\(J = 30\)).
Now we can substitute the value of J into our equation:
\[ 30 = 5 \times A \] To find the number of apples Adam has, solve for A:
\[ A = \frac{30}{5} \] \[ A = 6 \] Step 4: Final Answer:
Adam has 6 apples.