Millie bakes cakes and sells them at the local market - Junior Cycle Mathematics - Question 2 - 2021

The total ratio parts = 5 + 7 = 12.

First, we calculate the weight of each part:

$$\text{Weight of each part} = \frac{2.4 \text{ kg}}{12} = 0.2 \text{ kg}$$

Now, calculate the weight of sugar:

$$\text{Weight of sugar} = 7 \times 0.2 \text{ kg} = 1.4 \text{ kg} = 1400 ext{ grams}$$

Millie used 1400 grams of sugar.

Calculating the total cost for each offer:

Offer A:

• Price for 1 kg = €3.50
• Price for 6 kg = 6 × €3.50 = €21.00
• Special offer gives 3 bags for the price of 2:
  • 3 kg = 2 × €3.50 = €7.00
• She would need 2 bags for the remaining 3 kg = 2 × €3.50 = €7.00

Total cost = €7.00 + €7.00 = €14.00

Offer B:

• Price for each kg bag = €5.00
• Total cost for 6 kg = 6 × €5.00 = €30.00
• Special offer gives 20% off:
  • Discount = 20% of €30.00 = €6.00

Total cost after discount = €30.00 - €6.00 = €24.00

Better value: Offer A (€14.00) is better than Offer B (€24.00).

Let the cost price of each cake be C.

Profit is calculated as:

$$\text{Profit} = \text{Selling Price} - \text{Cost Price} = 0.20 \times C$$

Setting up the equation:

$$\text{Selling Price} = C + 0.20C \\ 7.50 = 1.20C$$

Now solving for C:

$$C = \frac{7.50}{1.20} = 6.25$$

The cost for Millie to make each cake is €6.25.

Using the formula for compound interest:

$$A = P \left(1 + \frac{r}{100}\right)^n$$

where:

• A = the amount of money accumulated after n years, including interest.
• P = principal amount (€3000).
• r = annual interest rate (2.5%).
• n = number of years (4).

Calculating:

$$A = 3000 \left(1 + 0.025\right)^4 = 3000 \times (1.025)^4$$

Calculating (1.025)^4:

$$(1.025)^4 \approx 1.10381289$$

Therefore,

$$A \approx 3000 \times 1.10381289 \approx 3311.44$$

After 4 years, the total amount in the account is approximately €3311.44.