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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineWanda wants to buy a charm bracelet. Rockport Fine Jewelry charges $10\$10 per charm, plus $96\$96 for the bracelet. Beck Jewelers, in contrast, charges $11\$11 per charm and $21\$21 for the bracelet. If Wanda 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?\newlineIf Wanda adds _____ charms to her bracelet, it will cost $\$_____ at either shop.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineWanda wants to buy a charm bracelet. Rockport Fine Jewelry charges $10\$10 per charm, plus $96\$96 for the bracelet. Beck Jewelers, in contrast, charges $11\$11 per charm and $21\$21 for the bracelet. If Wanda 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?\newlineIf Wanda adds _____ charms to her bracelet, it will cost $\$_____ at either shop.
  1. Define Cost Equations: Let xx be the number of charms Wanda adds to her bracelet. Rockport Fine Jewelry charges $10\$10 per charm plus $96\$96 for the bracelet, so the total cost at Rockport Fine Jewelry can be represented by the equation: 10x+9610x + 96.
  2. Set Up System of Equations: Beck Jewelers charges $11\$11 per charm and $21\$21 for the bracelet, so the total cost at Beck Jewelers can be represented by the equation: 11x+2111x + 21.
  3. Solve for x: Since the cost will be the same at either jewelry shop, we can set the two equations equal to each other to form a system of equations:\newline10x+96=11x+2110x + 96 = 11x + 21
  4. Substitute xx into Equation: To solve for xx, we will subtract 10x10x from both sides of the equation:\newline10x+96−10x=11x+21−10x10x + 96 - 10x = 11x + 21 - 10x\newlineThis simplifies to:\newline96=x+2196 = x + 21
  5. Calculate Total Cost: Next, we subtract 2121 from both sides of the equation to solve for xx: \newline96−21=x+21−2196 - 21 = x + 21 - 21\newlineThis simplifies to:\newline75=x75 = x
  6. Calculate Total Cost: Next, we subtract 2121 from both sides of the equation to solve for xx: \newline96−21=x+21−2196 - 21 = x + 21 - 21\newlineThis simplifies to:\newline75=x75 = xNow that we have the value of xx, which is 7575, we can calculate the total cost of the bracelet at either shop by substituting xx back into either of the original equations. Let's use the Rockport Fine Jewelry equation:\newlineTotal cost at Rockport = 10x+9610x + 96\newlineTotal cost at Rockport = 10(75)+9610(75) + 96
  7. Calculate Total Cost: Next, we subtract 2121 from both sides of the equation to solve for xx: \newline96−21=x+21−2196 - 21 = x + 21 - 21\newlineThis simplifies to:\newline75=x75 = xNow that we have the value of xx, which is 7575, we can calculate the total cost of the bracelet at either shop by substituting xx back into either of the original equations. Let's use the Rockport Fine Jewelry equation:\newlineTotal cost at Rockport = 10x+9610x + 96\newlineTotal cost at Rockport = 10(75)+9610(75) + 96Perform the calculation:\newlineTotal cost at Rockport = 750+96750 + 96\newlineTotal cost at Rockport = 846846

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