Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Bella wants to buy a charm bracelet. Norwood Fine Jewelry charges $13 per charm, plus $24 for the bracelet. Acosta Jewelers, in contrast, charges $12 per charm and $27 for the bracelet. If Bella wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. How many charms would that be? What would the total cost of the bracelet be?


If Bella adds charms to her bracelet, it will cost $ at either shop.

Answer 1

Total number of charms added would be 3.

Total cost of the bracelet = $ 63.

If Bella adds 3 charms to her bracelet, it will cost $ 63 at either shop.

Explanation:

Let the number of charms added be
`x`.

Total charge by Norwood Fine Jewelry for
`x` charms =
`13x + 24`

Total charge by Acosta Jewelers for
`x` charms =
`12x + 27`

If the charge by both the jewelers are to be same, then,

`13x+24=12x+27\\13x-12x=27-24\\x=3`

Therefore, 3 charms are added to the bracelet to make the total charge at either of the jewelry shop same.

Now, total charge at either of the jewelry shop for
`x=3` is:

Total charge =
`13(3)+24=39+24=63`

If Bella adds 3 charms to her bracelet, it will cost $ 63 at either shop.