n = Ken's age now
t = Kate's age now
j = Jean's age now
Ken was half as old as Kate x years ago so that
(n-x)/(t-x) = 1/2
n-x = (t-x)/2
n - t/2 = x/2
x = 2n - t
j-(2n-t) = 38
j-2n+t = 38
j = 2n - t + 38
Kate was half as old as Jean y years ago so that
(t-y)/(j-y) = 1/2
t-y = (j-y)/2
t - j/2 = y/2
y = 2t - j
n-(2t-j) = 17
n-2t+j = 17
j = 2t - n + 17
2t - n + 17 = 2n - t + 38
3t - 3n = 21
t - n = 7
t = n + 7
j = 2n - (n+7) + 38 = n + 31
j+t+n = 3n + 38
n 3n+38
1 41
2 44
3 47
4 50
5 53
6 56
7 59
8 62
9 65
10 68
11 71
12 74
13 77
14 80
15 83
16 86
17 89
18 92
19 95
20 98
21 101
22 104
23 107
24 110
25 113
26 116
27 119
28 122
29 125
30 128
Well, I didn't really need to construct a table (via calculator table function). However there was a suspicion that the total might have been 131 or even 311.
Ken is 25
Kate is 32
Jean is 56
---
113
Of course if Ken were 31, Kate would be 38 and Jean 87 for a total of 131, so the same digits would be used in the total.
18 years ago Ken was 7 and Kate 14; Jane was 38.
8 years ago Kate was 24 and Jane 48; Ken was 17.
This checks out.
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Posted by Charlie
on 2018-01-30 10:20:29 |
the algebra and a variation
