Ron had $35 with which he wanted to buy some chocolates priced at $2 per pieces, some pens priced at $ 5 per piece and some pencils priced at $4 per piece. What is the difference between the maximum number of total items he can buy and the minimum number of total items he can buy, if he must buy at least one chocolate one pen and one pencil and he must to spend the entire amount with him ?

Options

A. 5
B. 6
C. 7
D. 8

Answer

To solve the problem step by step, we will first determine the minimum and maximum number of items Ron can buy with his $35, given the constraints.

### Step 1: Calculate the minimum spending
Ron must buy at least:
- 1 chocolate at $2
- 1 pen at $5
- 1 pencil at $4

Calculating the total minimum spending:
\[ \text{Minimum spending} = 2 + 5 + 4 = 11 \text{ dollars} \]

### Step 2: Calculate the remaining amount
After spending the minimum amount, we find out how much money Ron has left:
\[ \text{Remaining amount} = 35 - 11 = 24 \text{ dollars} \]

### Step 3: Calculate the maximum number of items
To maximize the number of items, Ron should buy the cheapest item, which is chocolate at $2 each. The number of chocolates he can buy with the remaining $24 is:
\[ \text{Number of chocolates} = \frac{24}{2} = 12 \]

Adding the initial items (1 chocolate, 1 pen, 1 pencil):
\[ \text{Total maximum items} = 12 + 1 + 1 + 1 = 15 \]

### Step 4: Calculate the minimum number of items
To minimize the number of items, Ron should buy the most expensive items. He can buy:
- 4 pens at $5 each
- 1 pencil at $4

Calculating the total cost:
\[ \text{Cost of 4 pens} = 4 \times 5 = 20 \text{ dollars} \]
\[ \text{Cost of 1 pencil} = 4 \text{ dollars} \]
\[ \text{Total cost} = 20 + 4 = 24 \text{ dollars} \]

Adding the initial items (1 chocolate, 1 pen, 1 pencil):
\[ \text{Total minimum items} = 4 + 1 = 5 \]

### Step 5: Calculate the difference
Now, we find the difference between the maximum and minimum number of items:
\[ \text{Difference} = 15 - 5 = 10 \]

### Final Answer
The difference between the maximum number of total items he can buy and the minimum number of total items he can buy is **10**.

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