Let’s solve each problem step by step.
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Section A, Problem 1:
We start with 152 people total.
- Under 35: 83 people
→ So, 35 and over = 152 - 83 =
69
Under 35 group (83 people):
- Snowboard: 27
→ So, Ski = 83 - 27 =
56
35 and over group (69 people):
- Ski: 55
→ So, Snowboard = 69 - 55 =
14
✔ Filled in:
- Top right circle (Ski under 35):
56
- Middle left circle (35 and over):
69
- Bottom right circle (Snowboard 35 and over):
14
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Section A, Problem 2:
Total: 690
KS3: 420
→ So KS4 = 690 - 420 =
270
KS3 group (420):
- Walk: 100
- Bike: 180
→ Bus = 420 - 100 - 180 =
140
KS4 group (270):
- Bus: 135
- Bike: 90
→ Walk = 270 - 135 - 90 =
45
✔ Filled in:
- KS3 → Bus:
140
- KS4 total:
270
- KS4 → Walk:
45
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Section B, Problem 1:
Total students: 300
Grade 8: 130 → So Grade 7 = 300 - 130 =
170
Grade 8:
- Theme park: 35
→ Waterpark = 130 - 35 =
95
Total waterpark: 176
→ So Grade 7 waterpark = 176 - 95 =
81
→ Then Grade 7 theme park = 170 - 81 =
89
✔ Filled in:
- Year 7 total:
170
- Year 7 → Theme park:
89
- Year 7 → Waterpark:
81
- Year 8 total:
130
- Year 8 → Theme park:
35
- Year 8 → Waterpark:
95
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Section B, Problem 2:
Total people: 420
Adults: 165 → Children = 420 - 165 =
255
Children:
- Comedy: 101
- Romance: 62 (given as “62 of the 173 watching romance were children”)
→ So Action for children = 255 - 101 - 62 =
92
Romance total: 173
→ Adults watching romance = 173 - 62 =
111
Adults total: 165
So far: Romance = 111
Left for Comedy + Action = 165 - 111 =
54
Also given: Same number of adults watched comedy as action → so split 54 evenly:
→ Comedy adults = 27
→ Action adults = 27
Now check totals per movie:
Comedy total = adults (27) + children (101) =
128
Romance total = 173 (given)
Action total = adults (27) + children (92) =
119
Check sum: 128 + 173 + 119 = 420
✔
✔ Filled in:
- Adults total:
165
- Adults → Comedy:
27
- Adults → Romance:
111
- Adults → Action:
27
- Children total:
255
- Children → Comedy:
101
- Children → Romance:
62
- Children → Action:
92
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Final Answer:
Section A, Problem 1:
- Ski (Under 35): 56
- 35 and over total: 69
- Snowboard (35 and over): 14
Section A, Problem 2:
- Bus (KS3): 140
- KS4 total: 270
- Walk (KS4): 45
Section B, Problem 1:
- Year 7 total: 170
- Year 7 → Theme park: 89
- Year 7 → Waterpark: 81
- Year 8 total: 130
- Year 8 → Theme park: 35
- Year 8 → Waterpark: 95
Section B, Problem 2:
- Adults total: 165
- Adults → Comedy: 27
- Adults → Romance: 111
- Adults → Action: 27
- Children total: 255
- Children → Comedy: 101
- Children → Romance: 62
- Children → Action: 92
Parent Tip: Review the logic above to help your child master the concept of probability tree worksheet.
