Divide 24 in the ratio 7:5, write 24.60 as a fraction of 2870, write 1.92 as a percentage of 1.60, and calculate a 15% discount on 12.

To divide $24 in the ratio$7:5$, first find the total number of parts: Total parts$= 7 + 5 = 12$Next, find the value of one part: Value per part$= \frac{$24}{12} = $2$Now, multiply the value per part by each number in the ratio: First share$= 7 \times $2 = $14$Second share$= 5 \times $2 = $10$

The two amounts are $14 and$10.

To write $24.60 as a fraction of$2870, form the fraction and simplify it.

$$\frac{24.60}{2870}$$

Multiply the numerator and denominator by 100 to remove the decimal:

$$\frac{24.60 \times 100}{2870 \times 100} = \frac{2460}{287000}$$

Divide both by 10:

$$\frac{246}{28700}$$

Divide both by 2:

$$\frac{123}{14350}$$

Recognize that $123 = 3 \times 41$. Check if 14350 is divisible by 41:

$$14350 \div 41 = 350$$

So, the fraction can be simplified by dividing both numerator and denominator by 41:

$$\frac{3 \times 41}{350 \times 41} = \frac{3}{350}$$

To write $1.92 as a percentage of$1.60, divide $1.92 by$1.60 and multiply by $100\%$.

$$\frac{1.92}{1.60} \times 100\%$$ $$\frac{192}{160} \times 100\%$$

Divide both numerator and denominator by 16:

$$\frac{12}{10} \times 100\%$$ $$1.2 \times 100\% = 120\%$$

The original price is $12, and it is reduced by$15%$. First, calculate the discount amount: Discount$= 15% \text{ of } $12 = 0.15 \times $12 = $1.80$Next, subtract the discount from the original price to find the sale price: Sale price$= \text{Original price} - \text{Discount}$Sale price$= $12 - $1.80 = $10.20$

Alternatively, if the price is reduced by $15\%$, the sale price is $100\% - 15\% = 85\%$ of the original price.
Sale price = 85\% \text{ of } \12 = 0.85 \times $12 = $10.20$

a)

i) The two amounts are \boxed{\14 and $10}$.

ii) The fraction in its lowest terms is $\boxed{\frac{3}{350}}$.

iii) $1.92 as a percentage of$1.60 is $\boxed{120\%}$.

b)

i) The sale price of the book is \boxed{\10.20}$.