1. Modeling with Mathematics
The cost (in dollars) of making [tex]\(b\)[/tex] bracelets is represented by [tex]\(4 + 5b\)[/tex].
The cost (in dollars) of making [tex]\(b\)[/tex] necklaces is represented by [tex]\(8b + 6\)[/tex].

Write a polynomial that represents how much more it costs to make [tex]\(b\)[/tex] necklaces than [tex]\(b\)[/tex] bracelets.



Answer :

To determine how much more it costs to make [tex]\( b \)[/tex] necklaces than [tex]\( b \)[/tex] bracelets, we need to compare the cost of making [tex]\( b \)[/tex] necklaces to the cost of making [tex]\( b \)[/tex] bracelets.

1. Cost of making [tex]\( b \)[/tex] bracelets:
The cost function for [tex]\( b \)[/tex] bracelets is given by:
[tex]\[ 4 + 5b \][/tex]

2. Cost of making [tex]\( b \)[/tex] necklaces:
The cost function for [tex]\( b \)[/tex] necklaces is given by:
[tex]\[ 8b + 6 \][/tex]

3. Difference in cost between necklaces and bracelets:
To find how much more it costs to make [tex]\( b \)[/tex] necklaces than [tex]\( b \)[/tex] bracelets, we subtract the cost of making [tex]\( b \)[/tex] bracelets from the cost of making [tex]\( b \)[/tex] necklaces:
[tex]\[ (8b + 6) - (4 + 5b) \][/tex]

4. Simplify the expression:
We simplify the resulting expression step-by-step:
[tex]\[ (8b + 6) - (4 + 5b) = 8b + 6 - 4 - 5b \][/tex]

Combine like terms:
[tex]\[ 8b - 5b + 6 - 4 = 3b + 2 \][/tex]

So, the polynomial that represents how much more it costs to make [tex]\( b \)[/tex] necklaces than [tex]\( b \)[/tex] bracelets is:
[tex]\[ 3b + 2 \][/tex]