Question

You've spent $50 on bracelets to sell at the football game. You want to sell each bracelet for $3. Let `b` be the number of bracelets you sell. What is the inequality to determine how many bracelets you must sell to make a profit?

Answer 1

See a solution process below:

Explanation:

We can write the inequality as:

`$3b > $50`

We used the `>` operator because we want to make a profit which means we want to get back more than $50.

If the problem had stated we wanted to "at least break even" we would of used the `>=` operator.

To solve this we divide each side of the inequality by `color(red)($3)` to find `b` while keeping the inequality balanced:

`($3b)/color(red)($3) > ($50)/color(red)($3)`

`(color(red)(cancel(color(black)($3)))b)/cancel(color(red)($3)) > (color(red)(cancel(color(black)($)))50)/color(red)(color(black)(cancel(color(red)($)))3)`

`b > 50/3`

`b > 16.bar6`

However, because you cannot sell a fraction of a bracelet we need to round the answer up.

We need to sell at least 17 bracelets to make a profit.

`17 * $3 = $51`