if the cost of 3 chocolates and 2 cookies is $22 and that of 2 chocolates and 3 cookies is $18, what is the cost of cookies.​

$2

Step-by-step explanation:Express as two equations . Lex x Be chocolate and y be cookies.

3x+2y=22

2x+3y= 18

Common factor of 6 so times first ran by 2, second ran by 3 . Eliminate.

$2

Step-by-step explanation:

Let the cost of a chocolate and a cookie be $x and $y respectively.

Using the given information, form 2 equations and label them.

3x +2y= 22 (1)

2x +3y= 18 (2)

Now let's try to multiply both equations by a certain integer, such that the coefficient of x in both equations are the same. This allows us to eliminate the x term through subtraction.

(1) ×2:

6x +4y= 44 (3)

(2) ×3:

6x +9y= 54 (4)

(4) -(3):

6x +9y -(6x +4y)= 54 -44

Expand, simplify:

6x +9y -6x -4y= 10

5y= 10

Dividing both sides by 5:

y= 10 ÷5

y= 2

Thus, a cookie costs $2.

Note:

• Since we are only trying to find the value of y (cost of cookie), it is faster to eliminate the x term.

• If the signs of the coefficient of the term is opposite (e.g. -6 and 6), we can eliminate the term through addition.

Example:

-6x +4y= 44 (1)

6x +9y= 54 (2)

(1) +(2):

-6x +4y +6x +9y= 44 +54

13y= 98

y= 98 ÷13

y= 7.54 (3 s.f.)

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