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May someone please help I will give 30 points to who can answer fully, no download scam link either

May someone please help I will give 30 points to who can answer fully, no download-example-1

1 Answer

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We can write equations by rewriting the important phrases of information using variables. These variables make the equation look neater and it is faster to write a letter instead of constantly repeating 'cost of student tickets', for example.

The important pieces of information lies in the second last sentence of this question.

  • the tickets of your friend, her mom and her little sister costs a total of $23
  • the tickets of 2 adults and 3 students costs a total of $39

Now, let's rewrite them into equations.

Given

x= cost of adult tickets

y= cost of student tickets

Assuming that your friend and her little sister are students, the two equations are:

  • x +2y= 23 -----(1)
  • 2x +3y= 39 -----(2)

To convert these equations into slope-intercept form, move all the terms that are not y to the right-hand side of the equation before dividing both sides by the coefficient of y. This is to ensure that the coefficient of y is 1 and that your equation is in y= mx +c, where m is the slope and c is the y-intercept.

From equation (1):

x +2y= 23

2y= -x +23

Divide both sides by 2:


\bf{y = - (1)/(2) x + (23)/(2) }

From equation (2):

2x +3y= 39

3y= -2x +39

Divide both sides by 3:


\bf{y= - (2)/(3) x + 13}

The solution to the system of equations is the point at which the two lines intercept on the graph. I have attached the graph as an image.

The solution is (9, 7).

The x coordinate is the cost of an adult ticket, while the y coordinate is the cost of a student ticket. This means that adult tickets cost $9 and student/ child tickets cost $7.

May someone please help I will give 30 points to who can answer fully, no download-example-1
User Meir Maor
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