24. There are two ponds at the bottom of Gabrielle's garden, each containing frogs and toads. In one pond the ratio of frogs to toads is $3: 4$. In the other pond the ratio of frogs to toads is $5: 6$. Suppose there are 36 frogs in total. What then would be the largest possible total number of toads in the ponds?
A 48
B 46
C 44
D 42
E 40
24. B Since the ratios of frogs to toads in the two ponds are $3: 4$ and $5: 6$ respectively, the numbers of frogs and toads are $3 x$ and $4 x$ in the first pond and $5 y$ and $6 y$ in the second pond for some positive integers $x$ and $y$. Therefore, since there are 36 frogs in total, we have $3 x+5 y=36$. Since both 3 and 36 are multiples of $3, y$ is also a multiple of 3 and since $5 y \leq 36$ we have $y=3$ or 6 . If $y$ were $3, x$ would be 7 and the total number of toads would be $4 \times 7+6 \times 3=46$. Similarly, if $y$ were $6, x$ would be 2 and the total number of toads would be $4 \times 2+6 \times 6=44$. Hence, the largest possible number of toads in the ponds would be 46 .