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.)
