A large bag contains red, blue, green, and yellow candies. Seth grabbed a handful and counted 12 red, 15 blue, 6 green, and 7 yellow candies. If the bag contains a total of 800 candies, which is the best prediction for the total number of blue candies in the bag?
To find the best prediction for the total number of blue candies in the bag, we can use proportions.
The proportion of blue candies in Seth's handful can be calculated as:
Number of blue candies in the handful / Total number of candies in the handful = Number of blue candies in the bag / Total number of candies in the bag
Using the values given:
15 (number of blue candies in Seth's handful) / (12 + 15 + 6 + 7) (total number of candies in Seth's handful) = x (number of blue candies in the bag) / 800 (total number of candies in the bag)
Cross-multiplying the proportion, we get:
15 / (12 + 15 + 6 + 7) = x / 800
Simplifying the left side of the equation:
15 / 40 = x / 800
To find x (the number of blue candies in the bag), we can multiply both sides of the equation by 800:
(15 / 40) * 800 = x
Calculating the right side of the equation:
(15 * 800) / 40 = x
The best prediction for the total number of blue candies in the bag is 300.