The ratio of yellow to blue skittles in a bag is 5:9. If there are 12 more blue skittles in the bag than yellow skittles, how many yellow skittles are in the bag?

The number of yellow skittles in the bag is 15 yellow skittles

Step-by-step explanation:

The ratio of yellow to blue skittles in the bag is 5:9

The number of blue skittles in the bag = 12 + The number of yellow skittles in the bag

From the ratio of yellow to blue skittles in the bag, we have;

Fraction of the total skittles that are yellow = 5/(5 + 9) = 5/14

Fraction of the total skittles that are blue = 9/14

Whereby placing the number of yellow skittles as Y, and the number of blue skittles as B we have;

The number of blue skittles = Y + 12

The total number of skittles = Y + Y + 12 = 2·Y + 12

Whereby the fraction of the total skittles that are blue = 9/14, we have

9/14 × (2·Y + 12)  = Y + 12

9 × (2·Y + 12) = 14 × (Y + 12)

18·Y + 108 = 14·Y + 168

18·Y - 14·Y = 168 - 108 = 60

4·Y = 60

Y = 60/4 = 15

∴ The number of yellow skittles in the bag = 15

The number of blue skittles is given as = Y + 12 = 15 + 12 = 27.

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