Question

justify conclusions there are 21 goats and 35 chickens on a farm. if 5 more goats and 5 more chickens are added, is the ratio of goats to chickens the same? write an argument to defend your solution.

Explanation:

Step1: Calculate initial ratio

The initial ratio of goats to chickens is $\frac{21}{35}=\frac{3}{5}$ (dividing both numerator and denominator by 7).

Step2: Calculate new - ratio

After adding 5 more goats and 5 more chickens, the number of goats is $21 + 5=26$ and the number of chickens is $35 + 5 = 40$. The new ratio is $\frac{26}{40}=\frac{13}{20}$ (dividing both numerator and denominator by 2).

Step3: Compare ratios

Since $\frac{3}{5}=\frac{3\times4}{5\times4}=\frac{12}{20}$ and $\frac{12}{20}
eq\frac{13}{20}$, the ratios are not the same.

Answer:

No, the ratio of goats to chickens is not the same. The initial ratio of goats to chickens is $\frac{3}{5}$, and the new ratio after adding 5 more goats and 5 more chickens is $\frac{13}{20}$, and $\frac{3}{5}
eq\frac{13}{20}$.