Elimination problem

Question

A winter clothing store had a sale and Cory bought two pairs of gloves and four hats for $43. Mark bought two pairs of gloves and two hats for $30. How much did each pair of gloves and each hat cost?

Answer 1

2G + 4H = 43

2G + 2H = 30

 

 

Subtracts the second equation FROM the first equation:

 

 2H = 13

 H = 13/2 = 6.50

 

Substituting into the second equation:

  2G + 2(6.50) = 30

  2G + 13 = 30

 2G = 17

G = 17/2 = 8.50

 

Gloves cost $8.50; Hats cost 6.50

 

2(8.50) + 4(6.50) = 

 17 + 26 = 43

 

2(8.50) + 2(6.50) = 

17 + 13 = 30