Question

A jeweler is selling bracelets at an art convention. it costs $135 to obtain a booth at the convention. the cost to make a single bracelet is $4.50. the jeweler sells the bracelets for $12 each.

The inequality 12b > 135 + 4.50b represents the situation in which the jeweler makes a profit.

Answer 1

(a) Loss from selling 15 necklaces

(b)
`b > 18`

Explanation:

The question has missing details. (See the comment section for missing details)

Given

`12b > 135 + 4.50b`

Solving (a): Will she make a profit from 15 necklaces

To do this, we substitute 15 for b in
`12b > 135 + 4.50b`

`12 * 15 > 135 + 4.50 * 15`

`180 > 202.5`

The inequality is not true.

Hence, she'll make a loss from selling 15 necklaces

Solving (b): An expression that represents profit.

To do this, we solve for b in
`12b > 135 + 4.50b`

Collect Like Terms

`12b - 4.50b > 135`

`7.5b > 135`

Make b the subject

`b > (135)/(7.5)`

`b > 18`

This implies that to make a profit, she must sell more than 18 necklaces.