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?
12 cans of grape soda could be in the cooler.
The ratio of orange soda to the total number of cans is given as 3 to 8. This means that for every 3 cans of orange soda, there are 5 cans of grape soda (since 8 - 3 = 5), leading to the equation where grape soda must be a multiple of 5.
12 cans of grape soda satisfies the condition since, with 12 grape cans, the total number of cans becomes 3 (orange) + 12 (grape) = 15, which maintains the ratio of 3 to 8 when calculated (3/15 = 1/5, or 3 out of 8 total).
16 cans of grape soda would lead to a total of 3 (orange) + 16 (grape) = 19 cans. The ratio of orange to total would then be 3/19, which does not simplify to 3/8, thus violating the given ratio.
With 22 cans of grape soda, the total becomes 3 (orange) + 22 (grape) = 25 cans. The ratio is 3/25, which again does not equal 3/8. This option does not fit the stated requirements.
If there are 35 cans of grape soda, the total would be 3 (orange) + 35 (grape) = 38 cans. The ratio becomes 3/38, which does not match the required ratio of 3 to 8.
48 cans of grape soda results in a total of 3 (orange) + 48 (grape) = 51 cans. The ratio of orange to total is 3/51, which does not equal 3/8, thus not satisfying the conditions of the problem.
The only viable option for the number of cans of grape soda that maintains the specified ratio of orange soda to total cans is 12. All other choices fail to uphold the given ratio, highlighting the importance of proportional reasoning in solving ratio problems.
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