Question

A store sells 12 pens for \$15. How much will 30 pens cost at the same rate?

• A. \$30
• B. \$35
• C. \$37.50
• D. \$40

Hint:

In proportion problems, simplifying the initial ratio can make calculations easier. The ratio of cost to pens is \$15 to 12, which simplifies to \$5 to 4. So, every 4 pens cost \$5. Since 30 pens is 7.5 groups of 4 pens, the cost is \(7.5 \times \$5 = \$37.50\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a problem of direct proportion. The cost of the pens is directly proportional to the number of pens. We can solve it by finding the unit price or by setting up a ratio.
Step 2: Key Formula or Approach:
Method 1: Unit Price
1. Find the cost of one pen.
2. Multiply the unit cost by the desired number of pens.
Method 2: Proportion
Set up the equation: \(\frac{\text{Cost}_1}{\text{Quantity}_1} = \frac{\text{Cost}_2}{\text{Quantity}_2}\)
Step 3: Detailed Explanation:
Using the Unit Price Method:
Cost of 12 pens = \$15.
Cost of 1 pen = \(\frac{\$15}{12} = \$1.25\).
Cost of 30 pens = \(30 \times \$1.25 = \$37.50\).
Using the Proportion Method:
Let \(C\) be the cost of 30 pens.
\[ \frac{15}{12} = \frac{C}{30} \] Solve for \(C\):
\[ C = \frac{15 \times 30}{12} = \frac{450}{12} = \frac{225}{6} = \frac{75}{2} = 37.50 \] The cost is \$37.50.
Step 4: Final Answer:
At the same rate, 30 pens will cost \$37.50. This corresponds to option (C).