System of Linear Equations: Natalie's Jewelry Sales

How many bracelets and necklaces did Natalie sell at the arts and crafts festival?

If she sold 30 total pieces of jewelry

Final answer:

This question is about solving a system of linear equations derived from real-world context. We set up two equations based on total sales and total pieces of jewelry sold, and then solve the system to find how many of each type of jewelry Natalie sold.

Natalie's Jewelry Sales solution:

We can set up two equations based on the information given:

• 1. Total sales: $4(bracelets) + $8(necklaces) = $160
• 2. Total pieces of jewelry: bracelets + necklaces = 30

Explanation:

This question is an example of a system of linear equations, often seen in mathematics. By solving these equations simultaneously, we can find the number of bracelets and necklaces Natalie sold at the arts and crafts festival.

To solve the system of linear equations, we can use a method like substitution or elimination. Let's choose the elimination method for this problem:

• 1. Multiply the second equation by 4 to match the coefficient of bracelets:
- 4(bracelets) + 4(necklaces) = 120
• 2. Subtract this new equation from the first equation:
- ($4(bracelets) + $8(necklaces)) - (4(bracelets) + 4(necklaces)) = $160 - $120 - 4(necklaces) = $40 - necklaces = 10
• 3. Substitute the value of necklaces back into the second original equation to find the number of bracelets:
- bracelets + 10 = 30 - bracelets = 20

Therefore, Natalie sold 20 bracelets and 10 necklaces at the arts and crafts festival. She made a total of $160 from selling her jewelry.