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Martha wants to buy a charm bracelet. Princeton Fine Jewelry charges $\$30$ per charm, plus $\$50$ for the bracelet. Wong Jewelers, in contrast, charges $\$20$ per charm and $\$100$ for the bracelet. If Martha 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? Write a system of equations.

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Evaluate two-variable equations: word problems

Full solution

Q. Martha wants to buy a charm bracelet. Princeton Fine Jewelry charges

\$30

per charm, plus

\$50

for the bracelet. Wong Jewelers, in contrast, charges

\$20

per charm and

\$100

for the bracelet. If Martha 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? Write a system of equations.

Define Variables: Let's define variables: Let $x$ be the number of charms Martha wants. The total cost at Princeton Fine Jewelry (PFJ) is $\$30x + \$50$ . The total cost at Wong Jewelers (WJ) is $\$20x + \$100$ .
Write Equations: Write the equations for each store: $\newline$ $1$ . PFJ: $30x + 50$ $\newline$ $2$ . WJ: $20x + 100$
Set Equal: Set the equations equal to find when the costs are the same: $30x + 50 = 20x + 100$
Solve for x: Solve for x: $\newline$ $30x + 50 = 20x + 100$ $\newline$ $30x - 20x = 100 - 50$ $\newline$ $10x = 50$ $\newline$ $x = 5$
Substitute $x$ : Substitute $x = 5$ back into either store's equation to find the total cost: $\newline$ Using PFJ: $30(5) + 50 = 150 + 50 = 200$

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