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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineClare wants to buy a charm bracelet. Kingwood Fine Jewelry charges $8\$8 per charm, plus $39\$39 for the bracelet. Austin Jewelers, in contrast, charges $9\$9 per charm and $5\$5 for the bracelet. If Clare 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?\newlineThe cost of the bracelet will be $\$_____ if Clare adds _____ charms to it.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineClare wants to buy a charm bracelet. Kingwood Fine Jewelry charges $8\$8 per charm, plus $39\$39 for the bracelet. Austin Jewelers, in contrast, charges $9\$9 per charm and $5\$5 for the bracelet. If Clare 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?\newlineThe cost of the bracelet will be $\$_____ if Clare adds _____ charms to it.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of charms Clare adds to her bracelet.\newlineLet CC be the total cost of the bracelet with charms.\newlineNow we can write the system of equations based on the information given:\newlineFor Kingwood Fine Jewelry: C=8x+39C = 8x + 39\newlineFor Austin Jewelers: C=9x+5C = 9x + 5\newlineThe question_prompt: ＂What would the total cost of the bracelet be if Clare adds a certain number of charms to it, and how many charms would that be?＂
  2. Write Equations: To solve the system of equations using substitution, we need to set the two equations equal to each other since the cost CC is the same at either jewelry shop: 8x+39=9x+58x + 39 = 9x + 5
  3. Set Equations Equal: Now, we will solve for xx by subtracting 8x8x from both sides of the equation:\newline8x+39−8x=9x+5−8x8x + 39 - 8x = 9x + 5 - 8x\newlineThis simplifies to:\newline39=x+539 = x + 5
  4. Solve for x: Next, we subtract 55 from both sides to solve for xx: \newline39−5=x+5−539 - 5 = x + 5 - 5\newlineThis gives us:\newline34=x34 = x
  5. Substitute xx: Now that we have the value of xx, which is the number of charms, we can substitute it back into either of the original equations to find the total cost CC. We'll use the first equation:\newlineC=8x+39C = 8x + 39\newlineC=8(34)+39C = 8(34) + 39
  6. Calculate Total Cost: We calculate the total cost:\newlineC=8×34+39C = 8 \times 34 + 39\newlineC=272+39C = 272 + 39\newlineC=311C = 311
  7. Final Result: We have found that the total cost of the bracelet will be $311\$311 if Clare adds 3434 charms to it.

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