Question

. A jeweler has 100 necklaces and bracelets to sell at a flea market. Bracelets are selling for $5.75 each, and necklaces are $8.50 each. If the jeweler makes $685.00 after selling all of the items, how many of each type of jewelry did the jeweler sell?

Answer 1

60 bracelets

40 necklaces

Step-by-step explanation:

Let n = number of necklaces sold

Let b = number of bracelets sold

Given:

• Total number of items sold = 100

⇒ n + b = 100

Given:

• Sale price of bracelet = $5.75
• Sale price of necklace = $8.50
• Total sales = $685

⇒ 5.75b + 8.5n = 685

Rewrite n + b = 100 to make b the subject, substitute into 5.75b + 8.5n = 685 and solve for n:

⇒ b = 100 - n

⇒ 5.75(100 - n) + 8.5n = 685

⇒ 575 - 5.75n + 8.5n = 685

⇒ 575 + 2.75n = 685

⇒ 2.75n = 110

⇒ n = 40

Substitute found value for n into n + b = 100 and solve for b:

⇒ 40 + b = 100

⇒ b = 60

Answer 2

there are total 60 bracelets and 40 necklaces.

Step-by-step explanation:

let necklaces be x

let bracelets be y

make two equations from the given values:

• x + y → 100
• 5.75y + 8.50x → $685

solving steps:

x + y → 100

x → 100 - y

using substitution method:

5.75y + 8.5x → 685

5.75y + 8.5(100 - y) → 685

5.75y - 8.5y + 850 → 685

-2.75y → 685 - 850

-2.75y → -165

y → 60

Find x:

x + y → 100

x → 100 - 60

x → 40