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

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Solve a system of equations using substitution: word problems

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

\newline

Clare wants to buy a charm bracelet. Kingwood Fine Jewelry charges

\$8

per charm, plus

\$39

for the bracelet. Austin Jewelers, in contrast, charges

\$9

per charm and

\$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?

\newline

The cost of the bracelet will be

\$

_____ if Clare adds _____ charms to it.

Define Variables: Let's define the variables: $\newline$ Let $x$ be the number of charms Clare adds to her bracelet. $\newline$ Let $C$ be the total cost of the bracelet with charms. $\newline$ Now we can write the system of equations based on the information given: $\newline$ For Kingwood Fine Jewelry: $C = 8x + 39$ $\newline$ For Austin Jewelers: $C = 9x + 5$ $\newline$ The 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?＂
Write Equations: To solve the system of equations using substitution, we need to set the two equations equal to each other since the cost $C$ is the same at either jewelry shop: $8x + 39 = 9x + 5$
Set Equations Equal: Now, we will solve for $x$ by subtracting $8x$ from both sides of the equation: $\newline$ $8x + 39 - 8x = 9x + 5 - 8x$ $\newline$ This simplifies to: $\newline$ $39 = x + 5$
Solve for x: Next, we subtract $5$ from both sides to solve for $x$ : $\newline$ $39 - 5 = x + 5 - 5$ $\newline$ This gives us: $\newline$ $34 = x$
Substitute $x$ : Now that we have the value of $x$ , which is the number of charms, we can substitute it back into either of the original equations to find the total cost $C$ . We'll use the first equation: $\newline$ $C = 8x + 39$ $\newline$ $C = 8(34) + 39$
Calculate Total Cost: We calculate the total cost: $\newline$ $C = 8 \times 34 + 39$ $\newline$ $C = 272 + 39$ $\newline$ $C = 311$
Final Result: We have found that the total cost of the bracelet will be $\$311$ if Clare adds $34$ charms to it.