An evocative image of a young entrepreneur pondering in front of a blank canvas displayed on an easel. The background is a tidy and creative space full of art supplies like paintbrushes, a palette with a variety of paints, and canvases stacked against the wall. Illumination from a window on the side reveals a sunny summer day outside, further enhancing the mood of this home-based painting business. The entrepreneur, an East Asian boy around the age of 16, holds a paintbrush in one hand and a palette in the other as he contemplates his maiden piece for his business venture.

You want to start a summer business to earn money. What will you do? You have to

consider how much money you can afford to invest in this business, how much it
will cost you to make each item, and how much you’re going to charge for each
item. Research something that would be reasonable to make and sell with the start-up investment you have determined.
TASK 1
a) What is the total amount of money you are willing to invest in this business?
*I choose to invest $75 in this business.
b) What item are you going to make and sell? Why?
*I am going to make paintings. I have made a few pretty paintings in the past and I believe it would be fun!
c) Describe how your business will work. How much will it cost you to make each item? How much will you sell each item for?
*I will think of a theme, and I will base my drawing off of that theme. I will use the $75 to buy some painting supplies, such as my favorite paint colors, a few brushes, and some canvases. Therefore, it shouldn’t cost much to make a painting! I will put all of my effort into each painting, and sell them for about $15-$25, depending on the painting. I will sell my paintings to friends and family, and ask others to spread the word about my business!
d) Do you think your business will be profitable? Explain your answer.
*If I invest $75 into my business, and I sell my paintings for $15-$25, I would not have to sell many paintings to make more money than I invested in the first place. Therefore, I do believe my business would be profitable.

I finished the first part, but I need help with the first part of the 2nd,

In Task 1 you determined how much of your own money you’re willing to spend to
get your business started. This is your limit—when making your product you can’t exceed this amount.
TASK 2
a) Write an inequality that represents the fact that while making your product you can't exceed this spending limit.

can someone here help?? thanks guys xoxo

To make a profit on x paintings at $15 each, you will need

15x > 75
x > 5
If you sell them for $25 each, you will need
25x > 75
x > 3

So you will need to sell 3-5 paintings, depending on the price you charge.

On the other hand, if it costs you $3 to make a painting, then for x paintings, you need
3x <= 75
x <= 25
You cannot make more than 25 paintings

Thank you oobleck!!!

Yeah, this helped.

Do you guys have the rest of task 2?

Sure, I'd be happy to help with that. Here's an inequality that represents the spending limit for your business:

Cost to make each painting ≤ $75

This inequality ensures that the cost of making each painting does not exceed the total amount you are willing to invest in your business.

Certainly! In Task 1, you mentioned that you are willing to invest $75 in your business. To represent the fact that you cannot exceed this spending limit while making your product, you can write the following inequality:

Cost of making each item x Number of items ≤ $75

In this inequality, "Cost of making each item" represents the amount of money it costs you to make one painting, and "Number of items" represents the quantity of paintings you intend to create and sell. The total cost of making all the items (the left side of the inequality) must be less than or equal to $75 (the right side of the inequality), ensuring that you stay within your spending limit.

Remember to consider the cost of painting supplies, such as paint, brushes, and canvases, when calculating the cost of making each item.