Question

An artist is selling children's crafts. Necklaces cost $2.50 each, and bracelets cost $1.25 each. Select all the combinations of necklaces and bracelets that the artist could sell for exactly $20.00.

15 necklaces and 1 bracelet



8 necklaces and no bracelets



no necklaces and 16 bracelets



3 necklaces and 8 bracelets



no necklaces and 8 bracelets



5 necklaces and 6 bracelets

Answer 1

The artist could sell the following combinations of necklaces and bracelets for exactly $20.00: 8 necklaces and no bracelets, no necklaces and 16 bracelets, no necklaces and 8 bracelets, and 5 necklaces and 6 bracelets.

Step-by-step explanation:

To find the combinations of necklaces and bracelets that the artist could sell for exactly $20.00, we need to use a systematic approach.

1. Start with the highest possible number of necklaces and no bracelets. In this case, the cost of the necklaces alone would be 15 x $2.50 = $37.50, which exceeds $20.00. So, this combination is not possible.
2. Next, consider 8 necklaces and no bracelets. The cost of the necklaces alone would be 8 x $2.50 = $20.00, which matches exactly with the target amount. So, this combination is possible.
3. Continue with no necklaces and 16 bracelets. The cost of the bracelets alone would be 16 x $1.25 = $20.00, which matches exactly with the target amount. So, this combination is possible.
4. Move on to 3 necklaces and 8 bracelets. The cost of the necklaces alone would be 3 x $2.50 = $7.50, and the cost of the bracelets alone would be 8 x $1.25 = $10.00. The total cost would be $7.50 + $10.00 = $17.50, which is less than $20.00. So, this combination is not possible.
5. Next, consider no necklaces and 8 bracelets. The cost of the bracelets alone would be 8 x $1.25 = $10.00, which is less than $20.00. So, this combination is possible.
6. Finally, consider 5 necklaces and 6 bracelets. The cost of the necklaces alone would be 5 x $2.50 = $12.50, and the cost of the bracelets alone would be 6 x $1.25 = $7.50. The total cost would be $12.50 + $7.50 = $20.00, which matches exactly with the target amount. So, this combination is possible.

The combinations of necklaces and bracelets that the artist could sell for exactly $20.00 are:

• 8 necklaces and no bracelets
• No necklaces and 16 bracelets
• No necklaces and 8 bracelets
• 5 necklaces and 6 bracelets

Answer 2

8 necklaces and no bracelets, no necklaces and 16 bracelets, 5 necklaces and 6 bracelets

Step-by-step explanation:

15 necklaces and 1 bracelet equals $38.75

8 necklaces and no bracelets equals 20

no necklaces and 16 bracelets equals 20

3 necklaces and 8 bracelets equals 17.5

no necklaces and 8 bracelets equals 10

5 necklaces and 6 bracelets equals 20