11/15x + 44 = x
4/15x = 44
x = 44/(4/15)
x = 44 * (15/4)
x = 165
4/15x = 44
x = 44/(4/15)
x = 44 * (15/4)
x = 165
15/15 - 11/15 = 4/15
1 = 15/15
1. Start by finding a common denominator for 2/5 and 1/3. The least common multiple of 5 and 3 is 15. So, we can rewrite the fractions with the common denominator:
2/5 = 6/15
1/3 = 5/15
2. Now add the fractions:
6/15 + 5/15 = 11/15
3. So, Homer gave away 11/15 of the whole bag.
4. The remaining fraction of the bag is 4/15 (15/15 - 11/15 = 4/15).
5. We also know that he gave 44 jelly beans to Bart, which is equivalent to (44/15) * (15/15) = 44/15 of the whole bag.
6. Now, let's set up an equation to find the whole bag's quantity:
44/15 = 4/15 * quantity of the whole bag
7. To get the quantity of the whole bag, we can multiply both sides of the equation by 15/4:
(44/15) * (15/4) = (4/15 * quantity of the whole bag) * (15/4)
44/4 = quantity of the whole bag
8. Simplifying, we find that the quantity of the whole bag is:
11 = quantity of the whole bag
Therefore, Homer had a bag of 11 jelly beans to start with.