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UNIT 6: ITEM 6a

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Amir telah mendaftar keahlian di Farmasi Mahkota dengan bayaran RM10 untuk seumur hidup.  


Berapakah perbelanjaan Amir untuk vitamin tersebut selama setahun, termasuk yuran keahlian? (Anggap setiap bulan Amir memerlukan 30 biji kapsul vitamin.)   

Your answer

UNIT 6: ITEM 6b

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Amir ingin menebus poin bagi menanggung kos bayaran ahli. Berapakah bilangan **minimum** botol vitamin yang boleh dibeli oleh Amir?   


Your answer

UNIT 6: ITEM 6bi

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Terangkan jawapan anda.  

The image describes a point collection system for a membership card at a pharmacy. Here's a breakdown of the key details:

1. **Point Collection (Pengumpulan Poin):** 
   - 1 RM (Malaysian Ringgit) spent = 1 point.

2. **Point Redemption (Tebusan Poin):** 
   - 200 points = 1 RM.

### Problem Analysis

Let's solve the problems stated for Amir regarding his vitamin purchases and membership:

#### 6a. Annual Spending Including Membership Fee

To calculate Amir's total spending for vitamins and membership over a year:

- **Membership Fee:** RM10 (one-time lifetime fee).
- **Vitamin Consumption:** Amir needs 30 capsules each month. Let's assume he buys them in bottles.

First, we need to calculate Amir's monthly and yearly vitamin expenses, but the price per bottle isn't provided. We will assume each bottle contains 30 capsules (enough for one month). 

Let \( P \) be the price of one bottle of vitamins in RM.

- **Monthly Vitamin Cost:** \( P \) RM.
- **Yearly Vitamin Cost:** \( 12 \times P = 12P \) RM.

Thus, the total spending for Amir over one year, including the membership fee, is:

\[
\text{Total Annual Spending} = 12P + 10 \text{ RM}
\]

#### 6b. Minimum Number of Bottles to Redeem Membership Cost

To find the minimum number of bottles Amir needs to buy to accumulate enough points to cover the membership fee:

- **Points Needed to Cover RM10:** \( 10 \times 200 = 2000 \) points.
  
Since Amir earns 1 point per RM spent:

- **Points per Bottle:** \( P \) points (where \( P \) is the price of one bottle).
- **Number of Bottles Required:** \( \frac{2000}{P} \).

To ensure an integer result (since Amir cannot buy a fraction of a bottle), Amir needs to purchase at least \( \left\lceil \frac{2000}{P} \right\rceil \) bottles.

### 6bi. Explanation of the Calculation

For Amir to cover the RM10 membership fee using points, he must collect 2000 points. Since each RM spent earns him one point, the minimum amount he must spend is RM2000. If each bottle costs \( P \) RM, he earns \( P \) points per bottle, and therefore, the number of bottles needed is calculated as \( \frac{2000}{P} \). This ensures Amir has enough points to redeem for RM10.

If the exact price \( P \) of a vitamin bottle is given, we can calculate the exact number of bottles.

Would you like further details or assistance with specific calculations? 

### Related Questions:

1. What would Amir's total points be if he spends RM500 on vitamins in a year?
2. If Amir only buys enough vitamins for six months, how much would his total spending be, including the membership fee?
3. How much would Amir save in the second year, considering he doesn't have to pay the membership fee again?
4. What is the break-even point in terms of bottles purchased, where Amir's membership cost is effectively covered by points?
5. How many bottles would Amir need to buy to redeem RM50?

### Tip:
When dealing with point systems and memberships, always calculate both immediate and long-term benefits to understand the total cost and potential savings.

Calculate Amir's total annual spending on vitamins, including the membership fee at Farmasi Mahkota. Learn how many bottles Amir needs to purchase minimum to redeem his membership fee.

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