Question

Mark bought 12 boxes of paper clips and 10 packages of index cards for a

total cost of $61.70. Janice bought 15 boxes of paper clips and 7 packages of
index cards for a total cost of $55.40. Find the cost of one box of paper clips
and the cost of one package of index cards.

Answer 1

paper clips = $1.85

index cards = $3.95

Explanation:

Mark

12 paper clips = x

10 index cards = y

$61.70 total

Janice

15 paper clips = x

7 index cards = y

$55.40 total

12x + 10y = 61.70

15x + 7y = 55.40

*** you want to cancel out one of the letters

(12x + 10y = 61.70) * -7

(15x + 7y = 55.40) * 10

-84x -70y = -431.9

150x + 70y = 554.0

150x + 70y = 554.0

-84x -70y = -431.9

66x + 0 = 122.1

66x = 122.1

x = 122.1 ÷ 66

x = 1.85

plug it back in

15(1.85) + 7y = 55.40

27.75 + 7y = 55.40

7y = 55.40 - 27.75

7y = 27.65

y = 27.65 ÷ 7

y = 3.95