How many apples
A farmer packed some apples into bags. He filled 1/3 of the bags with 6 apples each, 1/2 of the bags with 4 apples each, and the remaining 4 bags with 10 apples each.
If he used a total of 36 bags, how many apples did he pack altogether?
Step 1: Find out how many bags are in each group.
ReplyDeleteTotal bags = 36
1/3 of 36 = 12 bags (with 6 apples each)
1/2 of 36 = 18 bags (with 4 apples each)
So far: 12 + 18 = 30 bags used
Remaining bags = 36 - 30 = 6 bags, but the question says 4 bags are left.
→ This shows a contradiction, so let’s check carefully.
Problem says:
1/3 of the bags → 6 apples each
1/2 of the bags → 4 apples each
Remaining 4 bags → 10 apples each
Let’s call the total number of bags = x
Then:
Bags with 6 apples = (1/3)x
Bags with 4 apples = (1/2)x
Bags with 10 apples = 4
So:
(1/3)x + (1/2)x + 4 = x
Step 2: Solve for x
Find a common denominator (LCD of 3 and 2 is 6):
(1/3)x = 2x/6
(1/2)x = 3x/6
So:
2x/6 + 3x/6 + 4 = x
(5x/6) + 4 = x
Now subtract 5x/6 from both sides:
4 = x - 5x/6
4 = x(1 - 5/6)
4 = x(1/6)
Multiply both sides by 6:
x = 24
Total bags = 24
Now calculate how many bags in each group:
1/3 of 24 = 8 bags with 6 apples
1/2 of 24 = 12 bags with 4 apples
Remaining = 24 - (8 + 12) = 4 bags with 10 apples ✅
Step 3: Calculate total apples
8 bags × 6 apples = 48 apples
12 bags × 4 apples = 48 apples
4 bags × 10 apples = 40 apples
Total = 48 + 48 + 40 = 136 apples