7. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Karen wants to buy a charm bracelet. Dazzling Diamonds charges \( \$ 17 \) per charm, plus \( \$ 54 \) for the bracelet. Jared's Jewelry charges \( \$ 16 \) per charm and \( \$ 65 \) for the bracelet. If Karen 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 Karen adds

Let \( x \) be the number of charms Karen wants to add. The total cost at Dazzling Diamonds can be expressed as: \[ C_1 = 17x + 54 \] The total cost at Jared's Jewelry is represented as: \[ C_2 = 16x + 65 \] To find when the costs are equal, we set the two equations equal to each other: \[ 17x + 54 = 16x + 65 \] Now, let's solve this equation using substitution. First, subtract \( 16x \) from both sides: \[ 17x - 16x + 54 = 65 \] This simplifies to: \[ x + 54 = 65 \] Next, subtract 54 from both sides to isolate \( x \): \[ x = 11 \] So, if Karen adds **11 charms**, the total cost for each jewelry shop can be calculated. Now plug \( x \) back into either equation. For Dazzling Diamonds: \[ C_1 = 17(11) + 54 = 187 + 54 = 241 \] Thus, the total cost of the bracelet would be **\$241**. Now let’s take a look at how charm bracelets have been a beloved accessory throughout history, often representing personal milestones or journeys. These bracelets have roots in ancient cultures, where charms were used for protection or as amulets! They evolved into fashion statements we cherish today! Did you know that charm bracelets originated in the 19th century as a symbol of protection? They later became popularized in the 20th century, bringing a new trend to the world of fashion! People began to collect charms that represented experiences, interests, or loved ones, making each bracelet a unique story of its own!