Mega movies hosted a film premiere on friday night. they charged $8 for adults and $5 for children. one hundred eight adults and children attended, and $777 was made in ticket sales. how many children and how many adults went to the film premiere?

Answers:

Number of adults = 79

Number of children = 29

Work Shown:

Let

x = number of adults

y = number of children

There are 108 total people, so x+y = 108. We can subtract x from both sides to isolate y and we get y = 108-x. We will use this equation later.

If we charge $8 per adult, then 8x represents all of the money pulled in from just the adults attending (ignoring the children for now)

Each child ticket costs $5, so 5y is the total money brought in from all the child ticket sales (ignore the adults temporarily)

In total, 8x+5y is the grand total for everyone that attends (adults and children). This grand total is given at 777 dollars.

Therefore, we know the second equation is 8x+5y = 777

Lets use substitution to eliminate the variable y

8x+5y = 777

8x+5( y ) = 777

8x+5( 108-x ) = 777 y replaced with 108-x

From here let's solve for x

8x+5( 108-x ) = 777

8x+5(108) + 5(-x) = 777 distributive property

8x + 540 - 5x = 777

8x - 5x + 540 = 777

3x + 540 = 777

3x + 540-540 = 777-540 subtracting 540 from both sides

3x = 237

3x/3 = 237/3 dividing both sides by 3

x = 79

Use this to find y

y = 108-x

y = 108-79 ... x is replaced with 79

y = 29

The two answers are x = 79 and y = 29. Meaning that 79 adults showed up along with 29 children.

Note how x+y = 79+29 = 108 which partially confirms our two answers. Plug (x,y) = (79,29) into the expression 8x+5y and you should find that the result is 777, which fully confirms the ordered pair solution.

-1/2 +2

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47