solve each problem by setting up and solving an appropriate system of equations. The income from a student production was $47,500

Burhan Hopper

Burhan Hopper

Answered question

2021-09-08

solve each problem by setting up and solving an appropriate system of equations. The income from a student production was $47,500. The price of a student ticket was $15, and nonstudent tickets were sold at $20 each. Three thousand tickets were sold. How many tickets of each kind were sold?

Answer & Explanation

irwchh

irwchh

Skilled2021-09-09Added 102 answers

Linear equation is an equation which has a single power on its variable, and if it contains only two variables then it is known as linear equation in two variables. for example: 5x+2y=16 here, x and y have a single power and there are two variables x and y so it is an example of linear equation in two variable .Let the number of student ticket sold be x. and, the number of non student tickets sold be y.

Now, according to the given condition total number of tickets sold is $3000. So, x+y=3000

Since price of a student ticket is $15. So, income from student ticket will be 15x. and since price of non student ticket is $20. So, income from non student ticket is 20y.

Now total income from the student production is $47500. from the above condition we get 15x+20y=47500

There are two linear system of equations which are:

x+y15x+20y=3000....(i)

47500....(ii)

Multiplying equation (i) by 15, we get

15x+15y=45000.....(iii)

Subtracting equation iii from equation ii we get 5y=2500

y=500

Now, putting y=500 in equation i we get x+500x=3000.

Hence, the number of student ticket sold be 2500 and the number of non ticket sold is 500.

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