Question

a vendor at the saturday market makes $9 profit on each necklace she sells and $5 profit on each bracelet.

1. find a combination of necklaces and bracelets that she could sell and make:

a. exactly $100 profit
necklaces: 10 and bracelets: 2 equal 100 profit. i started with 10 necklaces and 2
b. more than $100 profit
type here

1. write an equation whose solution is the combination of necklaces and bracelets she could sell and make exactly $100 profit. let

represent number of necklaces sold and b represent number of bracelets.
type your answer in the box.

Explanation:

Step1: Define variables for part 1a

Let $n$ = number of necklaces, $b$ = number of bracelets. Profit equation: $9n + 5b = 100$

Step2: Test valid integer values for 1a

Test $n=10$: $9(10) + 5b = 100 \implies 90 + 5b = 100 \implies 5b=10 \implies b=2$

Step3: Find values for 1b (profit >100)

Choose $n=11, b=2$: $9(11)+5(2)=99+10=109>100$

Step4: Write equation for part 2

Use defined variables to set up profit equality.

Answer:

1. a. 10 necklaces and 2 bracelets

b. 11 necklaces and 2 bracelets (or any valid combination where $9n+5b>100$, e.g., 10 necklaces and 3 bracelets, 12 necklaces and 0 bracelets)

1. $9n + 5b = 100$