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
What is a reasonable solution?
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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