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Two partners divide a profit of $3000 so that the difference between the two amounts is 1/3 their average (arithmetic mean). what is the ratio of the larger to the smaller amount?)

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midorimondol

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.

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