$986 in revenue for a play. Tickets for the play cost $10 for adults and $6 for students. The number of students attending the play was LaTeX: \frac{3}{4}\:\:\: 3 4 the number of adults attending the play. How many adults and students attended the play?


the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

Which are the possible side lengths of a triangle?
A’b’c’ are the coordinates to the new location of the transformed triangle abc. find the distance between the coordinates points to use for your calculations.
Triangle abc is transformed to obtain triangle a’b’c’

68 adults and 51 students attended the play.

Step-by-step explanation:

Let x = Number of adults

y= Number of students

As per given,

10x+6y=986\ \ \ \ (i)\\\\ y=\dfrac34x\ \ \ \ (ii)

Put (ii) in (i) , we get

10x+6(\dfrac34x)=986\\\\\Rightarrow\ 10x+\dfrac{9}{2}x=986\\\\\Rightarrow\dfrac{29}{2}x=986\\\\\Rightarrow\ x=\dfrac{986\times2}{29}\\\\\Rightarrow\ x=68

So, y=\dfrac{3}{4}\times68=51   (from (ii))

Hence, 68 adults and 51 students attended the play.

Do you know the answer?

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