Luke spendsa total of $41 on three drinks and 10 bags of popcorn christopher spend a total of $11 on two drinks and two bags of popcorn right assessment equations that can be used to find the price of one using these equations determine the state the price of the bag of popcorn to the nearest cent

System of equations that can be used to find the price of one drink and the price of one bag of popcorn is:

3d + 10p = 41

2d + 2p = 11

Price of a bag of popcorn is $ 3.5

Let "d" be the price of one drink

Let "p" be the price of 1 bag of popcorn

Luke spends total of $41 on three drinks and 10 bags of popcorn

3 drinks x price of one drink + 10 bags of popcorn x price of 1 bag of popcorn = 41

3d + 10p = 41 ------ eqn 1

Christopher spend a total of $11 on two drinks and two bags of popcorn

2 drinks x price of one drink + 2 bags of popcorn x price of 1 bag of popcorn = 11

2d + 2p = 11 ------- eqn 2

Eqn 1 and eqn 2 represents system of equations that can be used to find the price of one drink and the price of one bag of popcorn

Let us solve eqn 1 and eqn 2 to find values of "d" and "p"

Multiply eqn 2 by 5

10d + 10p = 55 --- eqn 3

Subtract eqn 3 from eqn 1

3d + 10p = 41

10d + 10p = 55

(-) ------------------------

-7d = -14

d = 2

From eqn 2,

2d + 2p = 11

2(2) + 2p = 11

4 + 2p = 11

2p = 7

p = 3.5

Thus price of 1 bag of popcorn is $ 3.5 and price of one drink is $ 2

answer: it is 1: 47 pm

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24