word problem help please? We can't figure this out...

Question

Boy spends $68 on trading cards. His collection contains 2 types of cards. Type A is $4 each, type B is $7 each.  how many packs of each type of trading cards were purchased if the total number of packs is 11?

Answer 1

4a + 7b = 68 (price function)

a + b = 11 (total number of packs purchased)

 

Now isolate a variable, plug into the other equation, and solve.

 

a = 11 -b

 

4(11-b) + 7b = 68

44 - 4b + 7b = 68

44 + 3b = 68

3b = 24

b = 8

 

a = 11-8 =3

 

Now double check your work by plugging your answers into the other equation.

 

4(3) + 7(8) = 68

12 + 56 = 68

68  = 68