Question

Mel paid $15.75 for 6 greeting

cards. Some of the cards cost
$2.50 each, and some cost $3.25
each. Let x represent the number
of cards that cost $2.50 each,
and y represent the number of
cards that cost $3.25 each. This
situation can be represented by
the system x + y = 6 and
2.5x + 3.25y = 15.75. How many
of each type of card did Mei
purchase?

Answer 1

Explanation:

x + y = 6 -------------(I)

y = 6 -x

2.5x + 3.25y = 15.75 -------------(II)

substitute y = 6 - x in equation (II)

2.5x + 3.25*(6 - x) = 15.75 {Distributive property: a(b +c) =a*b + b*c}

2.5x + 3.25*6 - x * 3.25 = 15.75

2.5x + 19.5 - 3.25x = 15.75

2.5x - 3.25x + 19.5 = 15.75 {Combine like terms}

-0.75x + 19.5 = 15.75

-0.75x=15.75 - 19.5

-0.75x = -3.75

x = -3.75/-0.75

x = 5

Plugin x = 5 in (I)

5 + y = 6

y = 6 - 5

y = 1