Page 155 - NUMINO Challenge_M2
P. 155
Answer
Key
3. Working Backwards
EEExxxeeerrrccciiissseee The tree grows twice as tall every year, so the height in 2007 can be
calculated by finding half the height every year starting from 2009 and
working backwards.
Height in 2007 Height in 2008 Height in 2009
2 ^2^2=4 (m)
The height in 2007, , is 1 m.
EEExxxeeerrrccciiissseee 1 chick moved from A to B, which took 1 away from A and added 1 to B. 3
chicks moved from B to A, which took 3 away from B and added 3 to A.
If the number of chicks that were originally in A is , and the number of
chicks that were originally in B is , then -1+3=5 and +1-3=5.
=3, =7
A: 3 chicks, B: 7 chicks
Type Study In one minute, the distance between the snails decreases by half. The
distance between the snails in the previous minute, then, is two times the
present distance. The distance between the snails at 3 minutes is 2 times
greater than the distance at 4 minutes: 3^2=6 cm.
The distance between the snails at 2 minutes is twice the distance at 3
minutes: 6 cm ^2=12 cm. The distance between the snails at 1 minute is
twice the distance at 2 minutes: 12^2=24 cm.
Distance at 2 minutes: 12 cm, Distance at 1 minute: 24 cm
The original distance of the snails is twice the distance at 1 minute.
24 cm ^2=48 cm
18 NUMINO Challenge M2
Key
3. Working Backwards
EEExxxeeerrrccciiissseee The tree grows twice as tall every year, so the height in 2007 can be
calculated by finding half the height every year starting from 2009 and
working backwards.
Height in 2007 Height in 2008 Height in 2009
2 ^2^2=4 (m)
The height in 2007, , is 1 m.
EEExxxeeerrrccciiissseee 1 chick moved from A to B, which took 1 away from A and added 1 to B. 3
chicks moved from B to A, which took 3 away from B and added 3 to A.
If the number of chicks that were originally in A is , and the number of
chicks that were originally in B is , then -1+3=5 and +1-3=5.
=3, =7
A: 3 chicks, B: 7 chicks
Type Study In one minute, the distance between the snails decreases by half. The
distance between the snails in the previous minute, then, is two times the
present distance. The distance between the snails at 3 minutes is 2 times
greater than the distance at 4 minutes: 3^2=6 cm.
The distance between the snails at 2 minutes is twice the distance at 3
minutes: 6 cm ^2=12 cm. The distance between the snails at 1 minute is
twice the distance at 2 minutes: 12^2=24 cm.
Distance at 2 minutes: 12 cm, Distance at 1 minute: 24 cm
The original distance of the snails is twice the distance at 1 minute.
24 cm ^2=48 cm
18 NUMINO Challenge M2
