Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Isabella wants to buy a charm bracelet. Springfield Fine Jewelry charges $13 per charm, plus $64 for the bracelet. Patton Jewelers, in contrast, charges $12 per charm and $67 for the bracelet. If Isabella 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 Isabella adds _____ charms to her bracelet, it will cost $_____ at either shop.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Isabella wants to buy a charm bracelet. Springfield Fine Jewelry charges $13 per charm, plus $64 for the bracelet. Patton Jewelers, in contrast, charges $12 per charm and $67 for the bracelet. If Isabella 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 Isabella adds _____ charms to her bracelet, it will cost $_____ at either shop.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables: Let x be the number of charms Isabella wants to add to her bracelet. Let y be the total cost of the bracelet with charms at either jewelry shop.  Now, we can write the equations for the total cost at each shop: Springfield Fine Jewelry: y = 13x + 64 Patton Jewelers: y = 12x + 67  The question_prompt: ＂How many charms would that be? What would the total cost of the bracelet be?＂Write Equations: To find the number of charms for which the cost is the same at both shops, we set the two equations equal to each other: 13x + 64 = 12x + 67Set Equations Equal: Now, we solve for x by subtracting 12x from both sides of the equation: 13x - 12x + 64 = 12x - 12x + 67 x + 64 = 67Solve for x: Next, we subtract 64 from both sides to isolate x: x + 64 - 64 = 67 - 64 x = 3Substitute x into Equation: Now that we have the number of charms (x), we can substitute it back into either of the original equations to find the total cost (y). Let's use the Springfield Fine Jewelry equation: y = 13x + 64 y = 13(3) + 64Calculate Total Cost: We calculate the total cost: y = 39 + 64 y = 103Final Result: We have found that if Isabella adds 3 charms to her bracelet, it will cost $103 at either shop.

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