Question

HELP MEEEEEEEEEE Package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards and 6 thank-you notes and costs $26.60. If x represents the cost of a birthday card and y represents the cost of a thank-you note, how much does each birthday card cost?{3x+2y=9.6 8x+6y=29.6 a $1.33 b $1.50 c $2.20 d $3.10

Answer 1

Answer: The correct option is

(c) $2.20.

Step-by-step explanation: Given that package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards and 6 thank-you notes and costs $26.60.

Also, x represents the cost of a birthday card and y represents the cost of a thank-you note.

We are to find the cost of each birthday card.

The system of linear equations representing the given situation is given by

`3x+2y=9.60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\8x+6y=26.60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Multiplying equation (i) by 3, we have

`3(3x+2y)=3*9.60\\\\\Rightarrow 9x+6y=28.80~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Subtracting equation (ii) from (iii), we get

`(9x+6y)-(8x+6y)=28.80-26.60\\\\\Rightarrow x=2.20.`

Thus, the cost of each birthday card is $2.20

Option (c) is CORRECT.

Answer 2

Each birthday card costs $2.2 ⇒ answer c

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