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

The total weight of the filling is 2.4 kg, which can be converted to grams:

$2.4 \text{ kg} = 2400 \text{ grams}$

The ratio of butter to sugar is 5:7, meaning for every 5 parts of butter, there are 7 parts of sugar. The total ratio parts are:

$5 + 7 = 12$

Now, we can find the weight of sugar:

$ext{Weight of Sugar} = \frac{7}{12} \times 2400 \text{ grams} = 1400 \text{ grams}$

Millie used 1400 grams of sugar.

To determine the better value for 6 kg of flour:

Offer A:

• 3 bags for the price of 2 means for 2 kg:

  • Price = €7.00 for 2 kg
  • Price per kg = $\frac{7}{2} = €3.50

  Total for 6 kg:

  • Price = $3.50 \times 6 = €21.00$

Offer B:

• 20% off the price of €5 per kg means:

  • Discounted price = $5 - (0.20 \times 5) = €4.00 per kg$

  Total for 6 kg:

  • Price = $4.00 \times 6 = €24.00$

Conclusion:

• Offer A gives Millie the better value as it costs €21.00 compared to €24.00 for Offer B.

To find the cost to make each cake, we use the profit formula:

$ext{Selling Price} = ext{Cost Price} + ext{Profit}$

The profit is 20% of the cost price, thus:

$7.50 = ext{Cost Price} + 0.20 \times ext{Cost Price} = 1.20 \times ext{Cost Price}$

Solving for the cost price:

$ext{Cost Price} = \frac{7.50}{1.20} = €6.25$

Millie costs €6.25 to make each cake.

To calculate the total amount after 4 years with compound interest, we use the formula:

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

Where:

• A = the amount of money accumulated after n years, including interest.
• P = principal amount (€3000)
• r = annual interest rate (decimal) (2.5% = 0.025)
• n = number of times that interest is compounded per year (1)
• t = number of years the money is invested (4)

Plugging in the values:

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

Calculating:

$\left(1.025\right)^{4} \approx 1.10381289$

Therefore:

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

The total amount in the account after 4 years, rounded to the nearest cent, is €3311.44.