book Maths Puzzle Numerical Ability

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Consider the lines l: {{{x = x(sub 0) + tv}}} and m: {{{x = x(sub 1) + su}}}. Show that l and m intersect if and only if {{{x(sub 0) - x(sub 1)}}} lies in

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problem:
(you have to use an equation to solve the problem)
the attendance at the ball game was 400 people. student tickets cost $2 and adult tickets cost $3. if $1050 was collected in ticket sales, how many of each type of ticket were sold?
x squared -3x +9