Question

The school that Imani goes to is selling tickets to the annual dance competition. On the first day of the ticket sales the school sold 7 adult tickets and 5 child tickets for a total of $96. The school took in $40 on the second day by seling 3 adult tickets . Find the price of an adult ticket and the price of a child ticket.
solve by using substitution elimination College prep algebra 2 math
heres the 2 equations i came up with 7x+5y=96 and 3x+2y= -40 show all work please
please help iv be stuck on this and anther one for days and if I get the 2 questions right I pass the class.

Answer 1

x =adult ticket price

y = child ticket price

I will assume you forget to put that they sold 2 child tickets on the second day

7x+5y=96 and 3x+2y= 40

I will use elimination.  Multiply the first equation by 2 and the second equation by -5 to eliminate y

2(7x+5y)=96*2

14x + 10y = 192

The second equation

-5(3x+2y)= 40*-5

-15x -10y = -200

Add the equations together

14x + 10y = 192

-15x -10y = -200

------------------------

-x = -8

Multiply by -1

x = 8

Now we need to find y

3x+2y= 40

3(8) +2y = 40

24+2y = 40

Subtract 24 from each side

24-24 +2y = 40-24

2y = 16

Divide by 2

2y/2 =16/2

y =8

The adult and the child ticket are both 8 dollars

Answer 2

Explanation:

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Extra info related to the question :-

What is a rationlising factor ?

If the product of two irrational numbers is a rational number then each of the the two is rationalising factor of the other.

What is the purpose of rationilising the denominator ?

If the denominator of a fraction is irrational it is somewhat difficult to locate the fraction on number line. So, to make it easy we need to rationalise the denominator.

How to rationalise the denominator ?

1) Consider the denominator of the fraction.

2) Then multiply the numerator and denominator with rationalising factor of the denominator.

______________________________________________________________________________

Extra info related to the question :-

What is a rationlising factor ?

If the product of two irrational numbers is a rational number then each of the the two is rationalising factor of the other.

What is the purpose of rationilising the denominator ?

If the denominator of a fraction is irrational it is somewhat difficult to locate the fraction on number line. So, to make it easy we need to rationalise the denominator.

How to rationalise the denominator ?

1) Consider the denominator of the fraction.

2) Then multiply the numerator and denominator with rationalising factor of the denominator.

_______________________________________