Max kept records about where he spent his money. At the end of the year, he announced that he had spent 1.2 of his income on food and rent, 1/2 of his income on clothing, 1/12 on entertainment, and had saved $1400.

Mike said he spent 1/2 of his income on food and rent, 1.4 of his income on clothing, 1/12 on entertainment, and had saved $1400.
1. Who had the highest yearly salary?
2.How much more did he make?
3. How much did the other person make during the year?

We need to find out how to solve this problem. We do not want the answer to the problem we want to know how to solve.

Confused about what you mean by

"he had spent 1.2 of his income on food.."

did you mean 1.2% ?
1.2 would be 120%, so he is obviously living beyond his means.
So is Mike.

please clarify.

(I am going to assume you meant:
Mike said he spent 1/2 of his income on food and rent, 1/4 of his income on clothing, 1/12 on entertainment, and had saved $1400. )

add up 1/2 + 1/4 + 1/12
subtract that from 1
whatever that fraction is represents $1400
divide 1400 by that fraction to get his income.
I got $8400

check:
1/2 of 8400 = 4200
1/4 of 8400 = 2100
1/12 of 8400 = 700
total so far = 7000 leaving 1400 for savings

I meant to type 1/2 and not 1.2,sorry. Thank you for answering the questions. I will use the same operation to solve the first part of the problem. Thank you!

To solve this problem, we need to set up equations based on the given information and then solve for the salaries of both Max and Mike. Here's how we can approach it step by step:

1. Let's assume Max's income is 'x'. Based on the given information, we can write the following equation for Max's expenses:
(1.2)x + (1/2)x + (1/12)x + 1400 = x

2. Simplifying the equation:
(1.2 + 1/2 + 1/12)x + 1400 = x

3. Combining the fractions:
(6/5 + 1/2 + 1/12)x + 1400 = x

4. Finding a common denominator for the fractions:
(72/60 + 30/60 + 5/60)x + 1400 = x
(107/60)x + 1400 = x

5. To isolate x, we can subtract (107/60)x from both sides of the equation:
1400 = x - (107/60)x

6. Simplifying the equation:
1400 = (60/60 - 107/60)x
1400 = (-47/60)x

7. To solve for x, we need to isolate it. Multiply both sides of the equation by (-60/47):
x = 1400 * (-60/47)

8. Calculate the value of x to find Max's annual salary.

Similarly, we can set up the same equation for Mike's expenses using the given information and solve for his salary. Then we can compare the two salaries to answer the questions about who had the highest salary and how much more one person made than the other.

Note: It is important to remember that the actual calculation is not provided here because we want to explain how to solve the problem, not the specific answer.