Let’s solve this step by step.
We have 4 Halloween objects:
- Black cat (let’s call it C)
- Pumpkin (P)
- Witch hat (H)
- Witch on broomstick (W)
Each is a different whole number from 1 to 7.
We are given 4 rows, each with 4 objects and their total:
Row 1: C + P + H + C = 23 → 2C + P + H = 23
Row 2: P + H + W + H = 20 → P + 2H + W = 20
Row 3: W + C + C + W = 26 → 2W + 2C = 26 → W + C = 13
Row 4: H + W + C + W = 24 → H + 2W + C = 24
From Row 3: W + C = 13 → So possible pairs for (W, C) since both are between 1–7 and different:
Only possibilities: (6,7), (7,6) — because 5+8=13 but 8 is too big; 4+9 invalid etc.
So either W=6, C=7 or W=7, C=6.
Try W=6, C=7:
Plug into Row 1: 2C + P + H = 23 → 2*7 + P + H = 23 → 14 + P + H = 23 → P + H = 9
Row 2: P + 2H + W = 20 → P + 2H + 6 = 20 → P + 2H = 14
Now we have:
P + H = 9
P + 2H = 14
Subtract first from second: (P + 2H) - (P + H) = 14 - 9 → H = 5
Then P = 9 - H = 4
Check if all values are different and ≤7:
C=7, W=6, H=5, P=4 → All different, all between 1–7 → Good!
Now check Row 4: H + 2W + C = 5 + 2*6 + 7 = 5 + 12 + 7 = 24 → Matches!
Perfect.
So:
Witch hat (H) = 5
Black cat (C) = 7
Pumpkin (P) = 4
Witch on broom (W) = 6
Final Answer:
Witch hat: 5
Black cat: 7
Pumpkin: 4
Witch on broom: 6
Parent Tip: Review the logic above to help your child master the concept of halloween math worksheet grade 4.
