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Primary 4 | Maths
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Current age is a multiple of 6.
(means 6 times a whole number that is bigger than 1)
Each group of 6 years can be split into 5 years and 1 year. The sum of all the 5 years is a multiple of 5 (for obvious reasons)
In order for the current age to be a multiple of 5 in 2 years time, the sum of all these 1 year and the 2 years that's added, must be a multiple of 5.
Taking away this 2 years, the sum of all those 1 year, is 2 less than a multiple of 5.
The number of 1 year is equal to the total sum of the 1 year
(number of groups x 1 year per group = number itself. Eg. 5 x 1 = 5)
This means the number of sets of 6 years (which is equal to the number of sets of 1 year) is 2 less than a multiple of 5.
So we test the following multiples of 5 where 2 is subtracted :
6 x (5 - 2) = 6 x 3 = 18
6 x (10 - 2) = 6 x 8 = 48
6 x (15 - 2) = 6 x 13 = 78
6 x (20 - 2) = 6 x 18 = 108
Since Minghui is more than 20 but less than 80 years old now, there are two possible answers : 48 and 78
Check :
48 + 2 = 50 = 5 x 10
78 + 2 = 80 = 5 x 16
Her age in 7 years time :
48 + 7 = 55
Or
78 + 7 = 85
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