Question 234636
Leah's age = A
Sue's age = B
John age = C

Equation 1: {{{A + B + C = 41}}}
Leah is 6 years older than so, that gives us equation 2.
Equation 2: {{{A = B + 6}}}
John is 5 years older than Leah, that gives us equation 3.
{{{C = A + 5}}}
You can rewrite John's age in terms of Sue.
C = A + 5 & A = B + 6
There fore C = B + 6 + 5
Substitute the new value for C into equation 1.
A + B + C = 41
{{{A + B + B + 6 + 5 = 41}}} Then substitute equation 2 in for A in equation 1.
A = B + 6
{{{B + 6 + B + B + 6 + 5 = 41}}} Combine like terms
{{{3B + 17 = 41}}} Substract 17 from both sides
{{{3B = 24}}} Divide both sides by 3
{{{B = 8}}}
Sue is 8