43. A picnic cooler contains cans of orange soda and cans of grape soda only. The ratio of the number of cans of orange soda in the cooler to the total number of cans of soda in the cooler is 3 to 8. Which of the following could be the number of cans of grape soda in the cooler?
Answer: A
The number of cans of grape soda in the cooler could be 12.
Given the ratio of orange soda to the total number of cans is 3 to 8, we can deduce that for every 3 cans of orange soda, there are 5 cans of grape soda (since 8 - 3 = 5). Therefore, if there are 12 cans of grape soda, this corresponds to 8 cans of orange soda, keeping the ratio intact.
A) 12
This option is correct because if there are 12 cans of grape soda, the total number of cans would be 12 (grape) + 8 (orange) = 20. This maintains the ratio of 3 to 8, as 8 is indeed 3/8 of 20.
B) 16
This option is incorrect. With 16 cans of grape soda, the total number of cans would be 16 + (3/5) * 16 = 16 + 9.6 = 25.6, which is not a whole number of cans, thus invalidating this option.
C) 22
This option is incorrect. If there were 22 cans of grape soda, the total number of cans would be 22 + (3/5) * 22 = 22 + 13.2 = 35.2, which is not a permissible whole number of cans.
D) 35
This option is incorrect. If there are 35 cans of grape soda, the total cans would be 35 + (3/5) * 35 = 35 + 21 = 56. This does not preserve the ratio of 3 to 8 because 21 is not 3/8 of 56.
E) 48
This option is incorrect. With 48 cans of grape soda, the total would be 48 + (3/5) * 48 = 48 + 28.8 = 76.8, which is not a whole number and fails to maintain the required ratio.
Conclusion
The only viable option that maintains the ratio of 3 to 8 is 12 cans of grape soda. All other options result in either non-integer totals or do not satisfy the ratio condition, confirming that A is the only correct choice.