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?

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absor201 absor201 · Answer 1 · 2020-02-12T10:53:46+01:00

The total cost of the bracelet will be $96.

The number of charms will be 2.

Step-by-step explanation:

Given,

Cost per charm at Dayton Fine Jewelry = $17

Cost of bracelet = $62

Let,

x be the number of charms

y be the total cost

y = 17x+62 Eqn 1

Cost per charm at Cain Jewelers = $18

Cost of bracelet = $60

y = 18x+60 Eqn 2

For same cost;

Eqn 1 = Eqn 2

[tex]17x+62=18x+60\\62-60=18x-17x\\2=x\\x=2[/tex]

Putting x=2 in Eqn 1

[tex]y=17(2)+62\\y=34+62\\y=96[/tex]

Putting x=2 in Eqn 2

[tex]y=18(2) +60\\y=36+60\\y=96[/tex]

The total cost of the bracelet will be $96.

The number of charms will be 2.

Keywords: equation, addition

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