Question

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.​

Answer 1

Answer:$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.

Answer 2

Answer:

$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.)