Middle School

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

Hana wants to buy a charm bracelet. Dayton Fine Jewelry charges $17 per charm, plus $62 for the bracelet. Cain Jewelers, in contrast, charges $18 per charm and $60 for the bracelet. If Hana 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 \( c \) be the number of charms.

For Dayton Fine Jewelry:
\[ \text{Cost} = 17c + 62 \]

For Cain Jewelers:
\[ \text{Cost} = 18c + 60 \]

Set the two equations equal to each other to find the number of charms:
\[ 17c + 62 = 18c + 60 \]

Solve for \( c \). Once \( c \) is determined, substitute it back into one of the original equations to find the total cost.

Answer :

Final answer:

To determine the number of charms for the bracelet to cost the same at both jewelry shops, we set up a system of equations and solved it using substitution. We found that Hana will need to add 2 charms, resulting in a total cost of $96 for the bracelet at either shop.

Explanation:

To determine the number of charms Hana can add to her bracelet such that the cost is the same at Dayton Fine Jewelry and Cain Jewelers, we need to set up a system of equations and solve using the substitution method.

System of Equations:

Let x represent the number of charms and y represent the total cost of the bracelet with charms.

Equation for Dayton Fine Jewelry: y = 17x + 62

Equation for Cain Jewelers: y = 18x + 60

Solution Using Substitution:

  1. Set the two equations equal to each other since the cost is the same:
    17x + 62 = 18x + 60
  2. Subtract 17x from both sides:
    62 = x + 60
  3. Subtract 60 from both sides to solve for x:
    x = 2
  4. Substitute x = 2 into either of the original equations to find y:
    y = 17(2) + 62
    y = 34 + 62
    y = 96

Hana will need to add 2 charms to her bracelet, and the total cost of the bracelet will be $96 at either jewelry shop.

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Rewritten by : Barada