Alan and Teresa are three years apart. The sum of their ages are between 35 and 57. How old can they both be?

Answer 1

Let Alan's age be a and Teresa's age be t

So |a - t| = 3

ie a - t = ±3

So a = t ±3

Also 35< a + t < 57

So 35 < 2t ±3 <57

So 35 < 2t +3 <57 when a = t + 3

ie 16 < t < 27 and so 19 < a < 30

OR 35 < 2t -3 <57 when a = t - 3

ie 19< t < 30 and 16 < a < 27

So if Teresa is older than Alan then her age lies between 19 and 30 and Alan's age lies between 16 and 27 such that whatever Teresa's age in these limits Alan's age is 3 years less than Teresa's

So a = t - 3 (19< t < 30)

AND if Teresa is younger than Alan then her age lies between 16 and 27 and Alan's age lies between 19 and 30such that whatever Teresa's age in these limits Alan's age is 3 years more than Teresa's

So a = t + 3 (16 < t < 27)

Answer 2

x= Alan's age
x+3 = Teresa's age
2x+3 = sum of ages
They could be 17 and 20, 18 and 21, 19 and 22, 20 and 23,
21 and 24, 22 and 25, 23 and 26, 24and 27, 25 and 28, and
26 and 29

I have assumed that by "between" you meant to exclude 35 and 57. If they are to be included then two more ages are possible:
30 and 27, and 16 and 19.

Answer 3

im sorry but their are a lot of numbers that can work here are some.

20 and 23=43
21 and 24= 45
22 and 25= 47
23 and 26= 49
24 and 27= 51

if you want more then mail me

Answer 4

BETWEEN 17 AND 28

17 AND 20
25 AND 28