Note: This method of doing this type of Guess & Check Problem Sums is almost the same as the Assumption Method. The only difference is that the Assumption Method does not ask for a table to be drawn. However, I've observed that many pupils who use the Assumption Method often don't get the correct answer. Drawing the table takes slightly longer but allows you to check that everything tallies.
Solution to GC1:
Triangles
(3 sides each)
|
Hexagons
(6 sides each)
|
Total
|
Check
|
|||
No
|
Sides
|
No
|
Sides
|
No
|
Sides
|
|
0
|
0
|
40
|
240
|
40
|
240
|
û
|
1
|
3
|
39
|
234
|
40
|
237
|
û (-3 per step)
|
40
|
159 (Target)
|
ü
|
||||
240 – 159 = 81 (Target difference)
81 ÷ 3 = 27 (No of Triangles)
40 - 27 = 13 (No of Hexagons) Ans: 27
triangles
Alternative solution to GC1:
Triangles
(3 sides each)
|
Hexagons
(6 sides each)
|
Total
|
Check
|
|||
No
|
Sides
|
No
|
Sides
|
No
|
Sides
|
|
40
|
120
|
0
|
0
|
40
|
120
|
û
|
39
|
117
|
1
|
6
|
40
|
123
|
û (+3 per step)
|
27
|
81
|
13
|
78
|
40
|
159 (Target)
|
ü
|
159 – 120 = 39 (Target difference)
39 ÷ 3 = 13 (No Hexagons)
40 – 13 = 27 (No of Triangles) Ans: 27
triangles
Solution to GC2:
Bags of 8 (8 sweets each) | Bags of 12 (12 sweets each) | Total | Check | |||
No of bags | No of sweets | No of bags | No of sweets | No of bags | No of sweets | |
25 | 200 | 0 | 0 | 25 | 200 | û |
24 | 192 | 1 | 12 | 25 | 204 | û (+4 per step) |
25 | 240 (Target) | ü | ||||
6 × 40 = 240 (Total number of sweets Don bought)
240 – 200 = 40 (Target difference)
40 ÷ 4 = 10 (No of Bags of 12)
25 – 10 = 15 (No of Bags of 8) Ans: 15 bags of 8
Alternative solution to GC2:
Bags of 8 (8 sweets each) | Bags of 12 (12 sweets each) | Total | Check | |||
No of bags | No of sweets | No of bags | No of sweets | No of bags | No of sweets | |
| 0 | 0 | 25 | 300 | 25 | 300 | û |
1 | 8 | 24 | 288 | 25 | 296 | û (-4 per step) |
25 | 240 (Target) | ü | ||||
6 × 40 = 240 (Total number of sweets Don bought)
300 – 240 = 60 (Target difference)
60 ÷ 4 = 15 (No of Bags of 8)
25 - 15 = 10 (No of Bags of 12) Ans: 15 bags of 8
Solution to GC3:
Ducks (2 legs each) | Cows (4 legs each) | Total | Check | |||
No | Legs | No | Legs | No | Legs | |
20 | 40 | 0 | 0 | 20 | 40 | û |
19 | 38 | 1 | 4 | 20 | 42 | û (+2 per step) |
24 | 8 | 20 | 56 (Target) | ü | ||
56 – 40 = 16 (Target difference)
16 ÷ 2 = 8 (No of Cows)
20 – 8 = 12 (No of Ducks) Ans(b): 12 ducks
Solution to GC4:
Shirts with 5 buttons | Shirts with 8 buttons | Total | Check | |||
No | Buttons | No | Buttons | No | Buttons | |
100 | 500 | 0 | 0 | 100 | 500 | û |
99 | 495 | 1 | 8 | 100 | 503 | û (+3 per step) |
235 | 53 | 100 | 659 (Target) | ü | ||
659 – 500 = 159 (Target difference)
159 ÷ 3 = 53 (No of shirts with 8 buttons)
100 – 53 = 47 (No of shirts with 5 buttons) Ans: 53 shirts have 8 buttons
Solution to GC5:
Girls (read 10 books each) | Boys (read 6 books each) | Total | Check | |||
No | Books | No | Books | No | Books | |
35 | 350 | 0 | 0 | 35 | 350 | û |
34 | 340 | 1 | 6 | 35 | 346 | û (-4 per step) |
140 | 21 | 35 | 266 (Target) | ü | ||
350 – 266 = 84 (Target difference)
84 ÷ 4 = 21 (No of Boys)
35 – 21 = 19 (No of Girls) Ans: 21 boys
Solution to GC6:
Adults ($25 each) | Children ($15 each) | Total | Check | |||
No | Amount | No | Amount | No | Amount | |
235 | 5875 | 0 | 0 | 235 | 5875 | û |
234 | 5850 | 1 | 15 | 235 | 5865 | û (-10 per step) |
1300 | 183 | 235 | 4045 (Target) | ü | ||
5875 – 4045 = 1830 (Target difference)
1830 ÷ 10 = 183 (No of Children)
235 – 183 = 52 (No of Adults) Ans: 183 children
Solution to GC7:
Horses (4 legs each) | Ostriches (2 legs each) | Total | Check | |||
No | Legs | No | Legs | No | Legs | |
157 | 628 | 0 | 0 | 157 | 628 | û |
156 | 624 | 1 | 2 | 157 | 626 | û (-2 per step) |
248 | 95 | 157 | 438 (Target) | ü | ||
314 ÷ 2 = 157 (No of animals on Peter's farm)
(All horses and ostriches have 2 eyes each)
628 – 438 = 190 (Target difference)
190 ÷ 2 = 95 (No of Ostriches)
157 – 95 = 62 (No of Horses) Ans: 62 horses
Solution to GC8:
20-cm long wire | 45-cm long wire | Total | Check | |||
No | Length | No | Length | No | Length | |
150 | 3000 | 0 | 0 | 150 | 3000 | û |
149 | 2980 | 1 | 45 | 150 | 3025 | û (+25 per step) |
1400 | 80 | 150 | 5000 (Target) | ü | ||
50 m = 5000 cm (Length of wire that is cut into 150 pieces)
5000 – 3000 = 2000 (Target difference)
2000 ÷ 25 = 80 (No of 45-cm long pieces)
150 – 80 = 70 (No of 20-cm long pieces) Ans: 70 pieces (20-cm long)
Solution to GC9:
Adults ($30 each) | Children ($12 each) | Total | Check | |||
No | Amount | No | Amount | No | Amount | |
367 | 11010 | 0 | 0 | 367 | 11010 | û |
366 | 10980 | 1 | 12 | 367 | 10992 | û (-18 per step) |
2370 | 288 | 367 | 5826 (Target) | ü | ||
11010 – 5826 = 5184 (Target difference)
5184 ÷ 18 = 288 (No of Children)
367 – 288 = 79 (No of adults) Ans: 288 children
Solution to GC10:
Sheep (4 legs each) | Chickens (2 legs each) | Total | Check | |||
No | Legs | No | Legs | No | Legs | |
405 | 1620 | 0 | 0 | 405 | 1620 | û |
404 | 1616 | 1 | 2 | 405 | 1618 | û (-2 per step) |
448 | 293 | 405 | 1034 (Target) | ü | ||
1620 – 1034 = 586 (Target difference)
586 ÷ 2 = 293 (No of Chickens)
405 – 293 = 112 (No of sheep) Ans: 112 sheep
