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Answer:
Let's say the two partners divide the profit into x and y, where x > y.
The difference between the two amounts is 1/3 their average, so we can write an equation:
x - y = (1/3) × (x + y)/2
Simplify the equation:
x - y = (1/6) × (x + y)
Multiply both sides by 6 to eliminate the fraction:
6x - 6y = x + y
Rearrange the equation to get all terms on one side:
5x - 7y = 0
Now, we know that the total profit is $3000, so x + y = 3000.
We can solve this system of equations using substitution or elimination. Let's use substitution.
Rearrange the second equation to isolate y:
y = 3000 - x
Substitute this expression for y into the first equation:
5x - 7(3000 - x) = 0
Expand and simplify:
5x - 21000 + 7x = 0
Combine like terms:
12x = 21000
Divide by 12:
x = 1750
Now that we have x, we can find y:
y = 3000 - x
= 3000 - 1750
= 1250
So, the larger amount is $1750 and the smaller amount is $1250.
The ratio of the larger to the smaller amount is:
1750 : 1250
= 7 : 5
Therefore, the ratio of the larger to the smaller amount is 7:5.