Question

Allen, Bill, and Carl split $2000 among them to be invested in different ways. Each begins with a different amount. At the end of one year, they have a total of $3000 dollars. Bill and Carl have both doubled their money, whereas Allen has managed to lose $200 dollars. What was Allen's original portion?​

Answer 1

This example is type of word problem of mathematics of linear equations in three variables. Here, let us assume that the amount received to Allen after splitting be 'x', the amount received by Bill be 'y' and the amount received by Carl be 'z'. As the total amount split between them is 2000. We get,

x + y + z = 2000 ------ (i)

Now, after one year,

Bill and Carl have doubled their money.

∴ 2y and 2z.

And Allen lost 200.

∴ (x-200)

Now, given that the total is 3000.

∴ x - 200 + 2y + 2z = 3000

∴ x + 2y + 2z = 2800  ----- (ii)

Substracting eq(i) from (ii), we have

y + z = 800

Substituting this value in eq(i),

x = 1200.

∴ Allen's original portion was $1200.