A jeweler must spend less than $300 to order gems for bracelets and necklaces. Supplies for each bracelet cost $5 and supplies for each necklace cost $12. This relationship is shown in the graph. The jeweler wants to make at least 10 more bracelets than necklaces. Which choice is a reasonable solution?
10 bracelets and 20 necklaces
10 bracelets and 30 necklaces
20 bracelets and 20 necklaces
20 bracelets and 10 necklaces
To solve the problem, we can set up the inequalities based on the information provided.
1. Cost Constraint: Let ( b ) be the number of bracelets and ( n ) be the number of necklaces. The cost inequality can be set up as follows:
[
5b + 12n < 300
]
2. Bracelet Constraint: The jeweler wants to make at least 10 more bracelets than necklaces:
[
b geq n + 10
]
Now, let’s analyze the choices given:
1. 10 bracelets and 20 necklaces:
[
5(10) + 12(20) = 50 + 240 = 290 < 300 quad text{(valid)}
]
[
10 geq 20 + 10 quad text{(invalid)}
]
2. 10 bracelets and 30 necklaces:
[
5(10) + 12(30) = 50 + 360 = 410 < 300 quad text{(invalid)}
]
3. 20 bracelets and 20 necklaces:
[
5(20) + 12(20) = 100 + 240 = 340 < 300 quad text{(invalid)}
]
4. **20 bracelets and