Answer:
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.
