Question

If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?

• A. 150/x
• B. 150x
• C. 6x
• D. 1500/x
• E. 600x

Hint:

In proportion problems involving different units (like dollars and cents), always convert them to a common unit before setting up your equation to avoid errors.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a rate problem that can be solved using proportions. We need to find the number of jellybeans per unit of cost and then apply it to the new amount of money.
Step 2: Key Formula or Approach:
We can set up a proportion: \[ \frac{\text{Jellybeans}_1}{\text{Cost}_1} = \frac{\text{Jellybeans}_2}{\text{Cost}_2} \] It is crucial to keep the units consistent (either all in dollars or all in cents).
Step 3: Detailed Explanation:
Let's keep the costs in dollars.
Cost\(_1\) = x dollars
Jellybeans\(_1\) = 300
Cost\(_2\) = 50 cents = $0.50
Jellybeans\(_2\) = J (this is what we want to find)
Now, set up the proportion: \[ \frac{300}{x} = \frac{J}{0.50} \] To solve for J, we can cross-multiply or simply multiply both sides by 0.50: \[ J = 0.50 \times \frac{300}{x} \] \[ J = \frac{0.50 \times 300}{x} \] \[ J = \frac{150}{x} \] Alternative Method (using cents):
x dollars = 100x cents
Cost\(_1\) = 100x cents
Cost\(_2\) = 50 cents
\[ \frac{300}{100x} = \frac{J}{50} \] Multiply both sides by 50: \[ J = 50 \times \frac{300}{100x} = \frac{15000}{100x} = \frac{150}{x} \] Step 4: Final Answer:
You can purchase 150/x jellybeans for 50 cents. The correct option is (A).