Create an engaging image that captures a financial regularity. Include elements of three different allocations: one involving food, represented by a grocery bag full of different types of produce; another focusing on living expenses, symbolized by a traditional key in a house-shaped keychain; and the last one concentrating on intellectual preservation, suggested by a stack of hardcover books in various colors. The balance at the end depicted by a small pile of money bills totaling $200. All elements are spread on a table in an orderly fashion, creating a narrative of frugal monthly budgeting, with no text included in the image.

A man spent 2/11 of his monthly salary on food, 3/8 of the remainder on rent and 1/9 of what still remaind on books. If he still had $200 left, find his salary per month.

1 - 2/11 = 11/11-2/11 = 9/11 remaining.

Rent = 3/8 * 9/11 = 27/88.
Bal. =5/8 * 9/11= 45/88.
Books = 1/9 * 45/88 = 5/88.
Bal. = 8/9 * 45/88 = 40/88 = 5/11.
5x/11 = 200.
5x = 2200
X = $440.

2/11 spent on food leaves 9/11

3/8 * 9/11 = 27/88 spent on rent ... 2/11 + 27/88 = 43/88, leaving 45/88
1/9 * 45/88 = 5/88 spent on books ... 43/88 + 5/88 = 6/11, leaving 5/11
So, if the salary is x, then
5/11 x = 200
and now just finish it off
check your answer to be sure it works.

Is what still remain equal to one?

Well, it sounds like this man is really good at budgeting... or he's just really hungry! Let's do some math and figure out his salary per month.

Let's represent his monthly salary as "x." He spends 2/11 of his salary on food, which leaves him with 9/11 of his salary.

Next, he spends 3/8 of the remainder on rent, leaving him with (9/11) * (5/8) = 45/88 of his salary.

Lastly, he spends 1/9 of what still remains on books, leaving him with (45/88) * (8/9) = 5/11 of his salary.

If we know that he still had $200 left, we can set up the equation:

(5/11)x = 200

Now, let's solve for x:

x = 200 * (11/5)
x = 440

So, his monthly salary is $440. I hope he's using some of that money to treat himself to a good meal!

To find the man's monthly salary, we need to work backwards from the given information.

Let's go through the solution step by step:

1. Start with the final amount the man had left, which is $200.

2. We are told that the man spent 1/9 of what still remained on books. This means that the remaining amount after rent was 1/9 of the total amount before spending on books.
Let's denote the remaining amount after rent as R1.

So, R1 = (8/9) * (remaining amount after food)

3. Similarly, we are told that the man spent 3/8 of the remainder on rent. This means that the remaining amount after spending on food was 5/8 of the total amount before spending on rent.
Let's denote the remaining amount after food as R2.

So, R2 = (5/8) * (total amount before spending on rent)

4. We are given that 2/11 of the monthly salary was spent on food. This means that the remaining amount after spending on food was 9/11 of the total amount before spending on food.
Let's denote the total amount before spending on food as T.

So, R2 = (9/11) * T

5. We know that R1 = (8/9) * R2, so substituting the value of R2 from step 4, we have:
R1 = (8/9) * (9/11) * T
= (8/11) * T

6. Finally, we know that R1 = $200, so substituting the value of R1 from step 5, we have:
(8/11) * T = $200

To find T, we multiply both sides of the equation by (11/8):

T = ($200) * (11/8)
≈ $275

Therefore, the man's monthly salary is approximately $275.