Question 714124: ‘That’s a question no gentleman should ask,’ she replied, ‘but I’ll tell you if you promise to keep it a secret.’ Alfred nodded, and his grandmother went on: ‘If you reverse my age you will get half of what I shall be in a year’s time.’
how old is gran
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! I'll make a couple of assumptions:
(1) Gran is <100
(2) Gran's age is a whole number
We will let 10x+y=Gran's age now
Then 10x+y+1=Gran's age in a year's time
And 10y+x=Gran's age reversed
Soooo:
10y+x=(1/2)(10x+y+1)
10y+x=5x+y/2 + 1/2 multiply each term by 2
20y+2x=10x+y+1 or
8x-19y+1=0 and
x=(19y-1)/8
Since we have only one equation with two unknowns, we'll just have to solve it by trial and error realizing that Gran's age is a whole number.
We assign values between 0-9 for y and when we have a whole number for x, we have a possible solution:
When we do this, we find that when y=3, x=7
So one possible solution is Gran is 73
CK
37=1/2(73+1)
37=(1/2)74
37=37
Sometimes with one equation and two unknowns, we can have more than one solution.
Hope this helps--ptaylor
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