Here are the solutions to the problems: b) Add: $123_{\text{five}} + 43_{\text{five}}$ Step 1: Add the numbers in base 5. When adding in base 5, if the sum of digits is 5 or more, we carry over groups of 5. $$ \begin{array}{r} 123_{\text{five}} \\ +\quad 43_{\text{five}} \\ \hline \end{array} $$ Rightmost column: $3 + 3 = 6$. In base 5, $6 = 1 \times 5 + 1$. Write down 1, carry over 1. Middle column: $2 + 4 + 1 (\text{carry}) = 7$. In base 5, $7 = 1 \times 5 + 2$. Write down 2, carry over 1. Leftmost column: $1 + 1 (\text{carry}) = 2$. Write down 2. The sum is $221_{\text{five}}$. The final answer is $\boxed{221_{\text{five}}}$. c) Given that $12_y = 7_{\text{ten}}$. Find the value of base $y$. Step 1: Convert the number $12_y$ from base $y$ to base 10. $$12_y = 1 \times y^1 + 2 \times y^0 = y + 2$$ Step 2: Set up the equation using the given information. $$y + 2 = 7$$ Step 3: Solve for $y$. $$y = 7 - 2$$ $$y = 5$$ The final answer is $\boxed{5}$. 24. The sum of 3 consecutive counting numbers is 63. Find the numbers. Step 1: Let the first counting number be $n$. The three consecutive counting numbers are $n$, $n+1$, and $n+2$. Step 2: Write the equation for their sum. $$n + (n+1) + (n+2) = 63$$ $$3n + 3 = 63$$ Step 3: Solve for $n$. $$3n = 63 - 3$$ $$3n = 60$$ $$n = \frac{60}{3}$$ $$n = 20$$ Step 4: Find the three consecutive numbers. The numbers are $n$, $n+1$, $n+2$. $20$, $20+1$, $20+2$. $20$, $21$, $22$. The final answer is $\boxed{20, 21, 22}$. 25. In a group of 50 farmers, $\frac{2}{5}$ grow crops and the rest rear animals. a) Find the fraction of the farmers that rear animals. Step 1: The total fraction of farmers is 1. Subtract the fraction that grow crops from 1 to find the fraction that rear animals. $$\text{Fraction rearing animals} = 1 - \text{Fraction growing crops}$$ $$\text{Fraction rearing animals} = 1 - \frac{2}{5}$$ $$\text{Fraction rearing animals} = \frac{5}{5} - \frac{2}{5}$$ $$\text{Fraction rearing animals} = \frac{3}{5}$$ The final answer is $\boxed{\frac{3}{5}}$. b) How many farmers grow crops? Step 1: Multiply the total number of farmers by the fraction that grow crops. $$\text{Number of farmers growing crops} = \frac{2}{5} \times 50$$ $$\text{Number of farmers growing crops} = 2 \times \frac{50}{5}$$ $$\text{Number of farmers growing crops} = 2 \times 10$$ $$\text{Number of farmers growing crops} = 20$$ The final answer is $\boxed{20 \text{ farmers}}$. c) How many more farmers rear animals than grow crops? Step 1: Calculate the number of farmers that rear animals. From part a), the fraction rearing animals is $\frac{3}{5}$. $$\text{Number of farmers rearing animals} = \frac{3}{5} \times 50$$ $$\text{Number of farmers rearing animals} = 3 \times \frac{50}{5}$$ $$\text{Number of farmers rearing animals} = 3 \times 10$$ $$\text{Number of farmers rearing animals} = 30$$ Step 2: Find the difference between the number of farmers rearing animals and the number of farmers growing crops. $$\text{Difference} = \text{Farmers rearing animals} - \text{Farmers growing crops}$$ $$\text{Difference} = 30 - 20$$ $$\text{Difference} = 10$$ The final answer is $\boxed{10 \text{ farmers}}$.