Francesca wants to buy a charm bracelet. Salem Fine Jewelry charges $19 per charm, plus $23 for the bracelet. Shepherd Jewelers, in contrast, charges $18 per charm and $98 for the bracelet. If Francesca wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. What would the total cost of the bracelet be? How many charms would that be?
Let's assume the number of charms Francesca wants to add to her bracelet is x.
The cost of the bracelet is $23.
The cost of each charm at Salem Fine Jewelry is $19, so the total cost of x charms at Salem Fine Jewelry is 19x.
The total cost at Salem Fine Jewelry is 23 + 19x.
The cost of each charm at Shepherd Jewelers is $18, so the total cost of x charms at Shepherd Jewelers is 18x.
The total cost at Shepherd Jewelers is 98 + 18x.
Since the cost is the same at both jewelry shops, we can set the two expressions equal to each other:
23 + 19x = 98 + 18x
Subtracting 18x from both sides gives:
23 + x = 98
Subtracting 23 from both sides gives:
x = 75
Plugging this value back into one of the expressions, we get:
Total cost = 23 + 19(75) = 23 + 1425 = $1448
Therefore, the total cost of the bracelet would be $1448 and the number of charms would be 75.