Question 393885
Let {{{a}}} = number of senior tickets sold
Let {{{b}}} = number of child tickets sold
Let {{{c}}} = number of adult tickets sold
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given:
{{{12a + 15b + 24c = 5670}}}
{{{c = 5a}}}
{{{b = 2a}}}
Now by substitution:
{{{12a + 15*(2a) + 24*(5a) = 5670}}}
{{{12a + 30a + 120a  = 5670}}}
{{{162a = 5670}}}
{{{a = 35}}}
and, since
{{{c = 5a}}}
{{{c = 175}}}
and, also
{{{b = 2a}}}
{{{b = 70}}}
35 senior, 70 child, and 175 adult tickets were sold
Check answer by plugging back into
{{{12a + 15b + 24c = 5670}}}