Answer:
Each birthday card costs $2.2 ⇒ answer c
Step-by-step explanation:
* Lets explain how to solve the problem
- Package A contains 3 birthday cards and 2 thank-you notes
- It costs $9.60
- Package B contains 8 birthday cards and 6 thank-you notes
- It costs $26.60
- x represents the cost of birthday card and y represents the cost of
thank-you note
* Lets change these information to two equations
∵ x represents the cost of each birthday cards
∵ y represents the cost of each thank-you notes
∵ Bag A contains 3 birthday cards and 2 thank-you notes
∵ Bag A costs $9.60
∴ 3x + 2y = 9.60 ⇒ (1)
∵ Bag B contains 8 birthday cards and 6 thank-you notes
∵ Bag B costs $26.60
∴ 8x + 6y = 26.60 ⇒ (2)
* Lets solve this system of equations to find x and y
- Multiply equation (1) by -3 to eliminate y
∵ -3(3x) + -3(2y) = -3(9.60)
∴ -9x - 6y = -28.8 ⇒ (3)
- Add equations (2) and (3)
∴ -x = -2.2
- Multiply both sides by -1
∴ x = 2.2
∵ x represents the cost of each birthday cards
∴ The cost of each birthday card is $2.2
* Each birthday card costs $2.2
