Page 113 - NUMINO Challenge_A2
P. 113
Answer
Key
Type Study Using Only One Side of the Balance
1 Sum of all the Given Weights 1 1 3 5 10 g
2 The measurable masses that can be found with the weights are shown below.
Weight Left Side of the Balance Measurable Mass
1
1
11 1 1 2
33
13 1 3 4
11 3 1135
15 1 5 6
11 5 1157
35 3 5 8
13 5 1359
11 3 5 1 1 3 5 10
Therefore, the measurable masses are 1 g, 2 g, 3 g, 4 g, 5 g, 6 g, 7 g, 8 g, 9 g, and 10 g.
Problem solving
1 Lisa and Tom have one 1-g, two 2-g, and one 4-g weights.
The masses that can be measured with the following number of weights are:
With one weight: 1 g, 2 g, and 4 g
With two weights: 1 2 3 g, 2 2 4 g, 1 4 5 g, 2 4 6 g
With three weights: 1 2 2 5 g, 1 2 4 7 g, 2 2 4 8 g
With four weights: 1 2 2 4 9 g
Therefore, the masses that can be measured are: 1 g, 2 g, 3 g, 4 g, 5 g, 6g, 7 g, 8 g, and 9 g.
8 NUMINO Challenge A2
Key
Type Study Using Only One Side of the Balance
1 Sum of all the Given Weights 1 1 3 5 10 g
2 The measurable masses that can be found with the weights are shown below.
Weight Left Side of the Balance Measurable Mass
1
1
11 1 1 2
33
13 1 3 4
11 3 1135
15 1 5 6
11 5 1157
35 3 5 8
13 5 1359
11 3 5 1 1 3 5 10
Therefore, the measurable masses are 1 g, 2 g, 3 g, 4 g, 5 g, 6 g, 7 g, 8 g, 9 g, and 10 g.
Problem solving
1 Lisa and Tom have one 1-g, two 2-g, and one 4-g weights.
The masses that can be measured with the following number of weights are:
With one weight: 1 g, 2 g, and 4 g
With two weights: 1 2 3 g, 2 2 4 g, 1 4 5 g, 2 4 6 g
With three weights: 1 2 2 5 g, 1 2 4 7 g, 2 2 4 8 g
With four weights: 1 2 2 4 9 g
Therefore, the masses that can be measured are: 1 g, 2 g, 3 g, 4 g, 5 g, 6g, 7 g, 8 g, and 9 g.
8 NUMINO Challenge A2
