System word problem with Subsitution

Question

Haley wants to buy a charm Richmond Fine Jewelry charges $30 per charm, plus $10 for the bracelet. Espinoza Jewelers, in contrast, charges $29 per charm and $12 for the bracelet. If Haley wants to add a certain number of charms to her bracelet, the cost will be the same either jewelry shop. What would the total cost ofthe bracelet be? How many charms would that be?

Answer 1

$30 charm plus $10 costs same as $29 charms plus $12 bracelet

 

30c + 10 = 29c + 12

        -10             -10

30c     =  29c +2

-29c       -29c

       c = 2

They cost the same when there are 2 charms..

 

2 charms + bracelet = 30x2 + 10 = 60 + 10 = 70

2 charms + bracelet = 29x2 + 12 = 58 + 12 = 70 (check with both equations)

The cost of the 2 charms and bracelet is $70