Dominic and Jose go to the movie theater and purchase refreshments for their
friends.
Dominic spends a total of $96.25 on 9 bags of popcorn and 8 drinks.
Jose spends a total of $85.25 on 3 bags of popcorn and 10 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn
and the price of one drink.
Using these equations, determine and state the price of a drink, to the nearest cent.

That's a lot of money to be spending at the movies.

96.25 = 9p + 8d

85.25 = 3p + 10d

That's our system.

Multiply second equation by 3,

255.75 = 9p + 30d

Subtract first equation

255.75 - 96.25  = 30d - 8d

159.5 = 22/d

d =  159.5/22 = 7.25

3p = 85.25 - 10d = 85.25 - 72.50 = 12.75

p = 4.25

Price of a drink is $7.25

Check:

9*4.25+8*7.25 = 96.25, good

3*4.25 + 10*7.25 = 85.25, good

4 puzzles in 3 hours

step-by-step explanation:

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841