Question: An artist is selling children’s crafts. Necklaces cost $2.25 each, and bracelets cost $1.50 per…

An artist is selling children’s crafts. Necklaces cost $2.25 each, and bracelets cost $1.50 per each. Select all the combinations of necklaces and bracelets that the artist could sell for exactly $12.00 A. 5 necklaces and 1 bracelet B. 2 necklaces and 5 bracelets C. 3 necklaces and 3 bracelets D. 4 necklaces and 2 bracelets E. 3 necklaces and 5 bracelets F. 6 necklaces and no bracelets G. No necklaces and 8 bracelets

Solution

To solve this problem, let \( x \) be the number of necklaces and \( y \) be the number of bracelets. The cost of a necklace is $2.25 and the cost of a bracelet is $1.50. We need to find all combinations where the total cost is $12.00. Setup the equation: \[ 2.25x + 1.50y = 12.00 \] Now check each option: A. \( x = 5, y = 1 \) \[ 2.25(5) + 1.50(1) = 11.25 + 1.50 = 12.75 \] B. \( x = 2, y = 5 \) \[ 2.25(2) + 1.50(5) = 4.50 + 7.50 = 12.00 \] C. \( x = 3, y = 3 \) \[ 2.25(3) + 1.50(3) = 6.75 + 4.50 = 11.25 \] D. \( x = 4, y = 2 \) \[ 2.25(4) + 1.50(2) = 9.00 + 3.00 = 12.00 \] E. \( x = 3, y = 5 \) \[ 2.25(3) + 1.50(5) = 6.75 + 7.50 = 14.25 \] F. \( x = 6, y = 0 \) \[ 2.25(6) + 1.50(0) = 13.50 + 0.00 = 13.50 \] G. \( x = 0, y = 8 \) \[ 2.25(0) + 1.50(8) = 0.00 + 12.00 = 12.00 \] The correct combinations are: - B. 2 necklaces and 5 bracelets - D. 4 necklaces and 2 bracelets - G. No necklaces and 8 bracelets