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?

Answer 1

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.