Question

Package A contains 3 birthday cards and 2 thank you notes and costs $18. Package B contains 8 birthday cards and 6 thank you notes and costs $50. 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?

Answer 1

Given:

Package A

Birthday cards = 3

Thank you notes = 2

Costs = $18

Package B

Birthday cards = 8

Thank you notes = 6

Costs = $50

Required:

x = birthday card cost

y = thank you notes cost

Solution:

Package A:

18 = 3x + 2y

Package B:

50 = 8x + 6y

Second, add the two equations using elimination method.

To find y eliminate x;

[8 (18 = 3x + 2y)] + [-3 (50 = 8x + 6y)]

(144 = 24x + 16y) + [-150 = -24x + (-18y)]

-6 = -2y

Divide both sides with -2.

y = 3 thank you notes cost

Next, let us find x by substituting the value of y.

(18 = 3x + 2y) + (50 = 8x + 6y)

[18 = 3x + 2(3)] + [50 = 8x + 6(3)]

(18 = 3x + 6) + (50 = 8x + 18)

68 = 11x + 24

68 – 24 = 11x

44 = 11x

Divide both sides with 11.

X = 4 birthday card cost