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 start from 0 for one of the items, and 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
|
|
1
|
3
|
39
|
234
|
40
|
237
|
û
|
2
|
6
|
38
|
228
|
40
|
234
|
û (-3 per step)
|
40
|
159 (Target)
|
ü
|
||||
237 – 234 = 3 (How much Total decrease per step)
234 – 159 = 75 (Total decrease needed to reach Target)
75 ÷ 3 = 25 (No of steps needed to reach Target)
2 + 25 = 27 (No of Triangles) Ans: 27
triangles
38 – 25 = 13 (No of Hexagons)
Alternative solution to GC1:
Triangles
(3 sides each)
|
Hexagons
(6 sides each)
|
Total
|
Check
|
|||
No
|
Sides
|
No
|
Sides
|
No
|
Sides
|
|
39
|
117
|
1
|
6
|
40
|
123
|
û
|
38
|
114
|
2
|
12
|
40
|
126
|
û (+3 per step)
|
27
|
81
|
13
|
78
|
40
|
159 (Target)
|
ü
|
126 – 123 = 3 (How much Total increase per step)
159 – 126 = 33 (Total increase needed to reach Target)
33 ÷ 3 = 11 (No of steps needed to reach Target)
38 – 11 = 27 (No of Triangles) Ans: 27
triangles
2 + 11 = 13 (No of
Hexagons)
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 | |
24 | 192 | 1 | 12 | 25 | 204 | û |
23 | 184 | 2 | 24 | 25 | 208 | û (+4 per step) |
25 | 240 (Target) | ü | ||||
6 × 40 = 240 (Total number of sweets Don bought)
208 – 204 = 4 (How much Total increases per step)
240 – 208 = 32 (Total increase needed to reach Target)
32 ÷ 4 = 8 (No of steps needed to reach Target)
38 – 8 = 15 (No of Bags of 8) Ans: 15
2 + 8 = 10 (No of Bags of 12)
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 | |
| 1 | 8 | 24 | 288 | 25 | 296 | û |
2 | 16 | 23 | 276 | 25 | 292 | û (-4 per step) |
25 | 240 (Target) | ü | ||||
6 × 40 = 240 (Total number of sweets Don bought)
296 – 292 = 4 (How much Total decrease per step)
292 – 240 = 52 (Total decrease needed to reach Target)
52 ÷ 4 = 13 (No of steps needed to reach Target)
2 + 13 = 15 (No of Bags of 8) Ans: 15
23 – 13 = 10 (No of Bags of 12)
Solution to GC3:
Ducks (2 legs each) | Cows (4 legs each) | Total | Check | |||
No | Legs | No | Legs | No | Legs | |
19 | 38 | 1 | 4 | 20 | 42 | û |
18 | 36 | 2 | 8 | 20 | 44 | û (+2 per step) |
24 | 8 | 20 | 56 (Target) | ü | ||
44 – 42 = 2 (How much Total increase per step)
56 – 44 = 12 (Total increase needed to reach Target)
12 ÷ 2 = 6 (No of steps needed to reach Target)
18 – 6 = 12 (No of ducks) Ans(a): 12 ducks
2 + 6 = 8 (No of cows) Ans(b): 8 cows
Solution to GC4:
Shirts with 5 buttons | Shirts with 8 buttons | Total | Check | |||
No | Buttons | No | Buttons | No | Buttons | |
99 | 495 | 1 | 8 | 100 | 503 | û |
98 | 490 | 2 | 16 | 100 | 506 | û (+3 per step) |
235 | 53 | 100 | 659 (Target) | ü | ||
506 – 503 = 3 (How much Total increase per step)
659 – 506 = 153 (Total increase needed to reach Target)
153 ÷ 3 = 51 (No of steps needed to reach Target)
98 – 51 = 47 (No of shirts with 5 buttons)
2 + 51 = 53 (No of shirts with 8 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 | |
34 | 340 | 1 | 6 | 35 | 346 | û |
33 | 330 | 2 | 12 | 35 | 342 | û (-4 per step) |
140 | 21 | 35 | 266 (Target) | ü | ||
346 – 342 = 4 (How much Total decrease per step)
342 – 266 = 76 (Total decrease needed to reach Target)
76 ÷ 4 = 19 (No of steps needed to reach Target)
33 – 19 = 14 (No of girls)
2 + 19 = 21 (No of boys) Ans: 21 boys
Solution to GC6:
Adults ($25 each) | Children ($15 each) | Total | Check | |||
No | Amount | No | Amount | No | Amount | |
234 | 5850 | 1 | 15 | 235 | 5865 | û |
233 | 5825 | 2 | 30 | 235 | 5855 | û (-10 per step) |
1300 | 183 | 235 | 4045 (Target) | ü | ||
5865 – 5855 = 10 (How much Total decrease per step)
5855 – 4045 = 1810 (Total decrease needed to reach Target)
1810 ÷ 10 = 181 (No of steps needed to reach Target)
233 – 181 = 52 (No of adults)
2 + 181 = 183 (No of children) Ans: 183 children
Solution to GC7:
Horses (4 legs each) | Ostriches (2 legs each) | Total | Check | |||
No | Legs | No | Legs | No | Legs | |
156 | 624 | 1 | 2 | 157 | 626 | û |
155 | 620 | 2 | 4 | 157 | 624 | 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)
626 – 624 = 2 (How much Total decrease per step)
624 – 438 = 186 (Total decrease needed to reach Target)
186 ÷ 2 = 93 (No of steps needed to reach Target)
155 – 93 = 62 (No of horses) Ans: 62 horses
2 + 93 = 95 (No of ostriches)
Solution to GC8:
20-cm long wire | 45-cm long wire | Total | Check | |||
No | Length | No | Length | No | Length | |
149 | 2980 | 1 | 45 | 150 | 3025 | û |
148 | 2960 | 2 | 90 | 150 | 3050 | û (+25 per step) |
1400 | 80 | 150 | 5000 (Target) | ü | ||
50 m = 5000 cm (Length of wire that is cut into 150 pieces)
3050 – 3025 = 25 (How much Total increase per step)
5000 – 3050 = 1950 (Total increase needed to reach Target)
1950 ÷ 25 = 78 (No of steps needed to reach Target)
148 – 78 = 70 (No of 20-cm long pieces) Ans: 70 pieces (20-cm long)
2 + 78 = 80 (No of 45-cm long pieces)
Solution to GC9:
Adults ($30 each) | Children ($12 each) | Total | Check | |||
No | Amount | No | Amount | No | Amount | |
366 | 10980 | 1 | 12 | 367 | 10992 | û |
365 | 10950 | 2 | 24 | 367 | 10974 | û (-18 per step) |
2370 | 288 | 367 | 5826 (Target) | ü | ||
10992 – 10974 = 18 (How much Total decrease per step)
10974 – 5826 = 5148 (Total decrease needed to reach Target)
5148 ÷ 18 = 286 (No of steps needed to reach Target)
365 – 286 = 52 (No of adults)
2 + 286 = 288 (No of children) Ans: 288 children
Solution to GC10:
Sheep (4 legs each) | Chickens (2 legs each) | Total | Check | |||
No | Legs | No | Legs | No | Legs | |
404 | 1616 | 1 | 2 | 405 | 1618 | û |
403 | 1612 | 2 | 4 | 405 | 1616 | û (-2 per step) |
448 | 293 | 405 | 1034 (Target) | ü | ||
314 ÷ 2 = 157 (No of animals on Peter's farm)
(All horses and ostriches have 2 eyes each)
1618 – 1616 = 2 (How much Total decrease per step)
1616 – 1034 = 582 (Total decrease needed to reach Target)
582 ÷ 2 = 291 (No of steps needed to reach Target)
403 – 291 = 112 (No of sheep) Ans: 112 sheep
2 + 291 = 293 (No of chickens)
