I need help

(b) Write an inequality to show how many snacks of one type would need to be sold to earn a profit of at least $500. Support your inequality with an explanation.

Info:

The club sold the snacks for $3 each. The club gets half of this amount as profit. The club also gets a bonus of $100 for any snack when it sells at least 200 of that snack. Last year’s data on sales are shown in the table.

Type of Snack Number sold
Energy Bars: 194
Baked chips: 200
Organic treats: 235
Whole grain crackers: 78

Question

I need help


(b) Write an inequality to show how many snacks of one type would need to be sold to earn a profit of at least $500. Support your inequality with an explanation.

Info: 

The club sold the snacks for $3 each. The club gets half of this amount as profit. The club also gets a bonus of $100 for any snack when it sells at least 200 of that snack. Last year’s data on sales are shown in the table.

Type of Snack               Number sold
Energy Bars:                  194
Baked chips:                  200
Organic treats:               235
Whole grain crackers:     78

anonymous · Answer

I'd really appreciate if anyone can take the time to read it, I just have to make an inequality expression and solve it

anonymous · Answer

Take all the time you need, not too long though ^_^

anonymous · Answer

I kind of got half way through: (more than and equal sign) 500 

I don't get the first part though

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

Was there a part (a) and anything before this?

anonymous · Answer

Yes, (a) Which snack(s) earned a profit of at least $350? Show your work.

jim_thompson5910 · Answer

ok so for part (b), if we made x the number of snacks sold, then how much money do we make if each snack is sold for $3 ?

anonymous · Answer

wait so would the expression be 3x (more than or equal sign) 500?

jim_thompson5910 · Answer

close, there are a few missing pieces though

jim_thompson5910 · Answer

`The club gets half of this amount as profit. `

so we take the `3x` and cut that in half to get `3x/2`

jim_thompson5910 · Answer

now what is the value of `3x/2` when x = 200 ?

anonymous · Answer

300?

jim_thompson5910 · Answer

yes, since that isn't 500 or more, we haven't reached the target

but there's a $100 bonus when 200 snacks are sold

but 300+100 = 400 is still not enough, which means you need to sell more snacks

jim_thompson5910 · Answer

in the end, the inequality set up will be 

$$\Large \frac{3x}{2} + 100 \ge 500$$

anonymous · Answer

ah ok

anonymous · Answer

So that's all? If so, that was fast! Thanks

jim_thompson5910 · Answer

yeah that's all there is to it

3x/2 is the profit made, then you add on the $100 bonus (it's added on because 200 snacks aren't enough to reach $500 profit, so more need to be sold)

anonymous · Answer

Ok, thanks for the explanation! Helped a lot!!

jim_thompson5910 · Answer

no problem