Question 235149
Setup:
A = # of tiickets that cost $21
B = # of tickets that cost $27
Equation 1: {{{21*A + 27*B = 675}}}
Equation 2: {{{ A + B = 29}}}

Solution:
Solve equation 2 for one of the variables.  I picked A
{{{ A + B = 29}}}
{{{ A = 29 - B}}}
Now plug (29-B) into equation 1 for A
{{{21*A + 27*B = 675}}}
{{{21*(29-B) + 27*B = 675}}}  Simplify the equation
{{{609 - 21B + 27B = 675}}}  Simplify again
{{{609 + 6B = 675}}}  Subtract 609 from both sides
{{{6B = 66}}} Divide both sides by 6
{{{B = 11}}}
Now plug 11 into equation 2 for B
{{{ A + B = 29}}}
{{{ A + 11 = 29}}}
{{{A = 18}}}
Check your answer
{{{21*A + 27*B = 675}}}
{{{21*18 + 27*11 = 675}}}
{{{378 + 297 = 675}}}
{{{675 = 675}}}