Allen, bill, and carl split 2000 dollars among them to invest in different ways. each begins with a different amount. at the end of one year their total is 3000 dollars. bill and carl have both doubled their money, whereas Allen has managed to lose 200 dollars. what was Allen's original portion?
Answers
Answer:
We know that
(x
2
+y
2
+z
2
+2xy+2yz+zx)=(x+y+z)
2
(i) 4x
2
+9y
2
+16z
2
+12xy−24yz−16xz
=(2x)
2
+(3y)
2
+(−4z)
2
+2(2x)(3y)+2(3y)(−4z)+2(−4z)(2x)
=(2x+3y−4z)
2
=(2x+3y−4z)(2x+3y−4z)
Answer:
Allen's original portion = 1400 dollars
Step-by-step explanation:
Given data
Allen, bill, and carl split 2000 dollars among them to invest in different ways and each one begins with a different amount
at the end of one year their total amount = 3000 dollars.
Bill and carl have both doubled their money,
Allen has managed to lose 200 dollars.
Here we need to find Allen's original portion
Let x y and z be the portions of the Allen, Bill, and carl respectively
from given data x+ y+ z = 2000 _ (1)
At end of the year
Bill and carl have doubled their money
⇒ Then Bill amount at end of the year = 2y
Carl amount at end of the year = 2z
Alien has lose 200 dollars
⇒ then Alien amount at end of the year = x - 200
We know that total amount at end of the year = 3000
x -200 + 2y+ 2z = 3000
x + 2y + 2z = 300 + 200
x + 2y + 2z = 3200 _(2)
⇒ do (1) - (2) ⇒ x+ y+ z - x - 2y -2z = 2000 - 3200
⇒ - 2y - 2z = -1200
⇒ -2( y+z) = -1200
⇒ y + z = 600_ (3) [ divided by -2 ]
substitute y + z = 600 in (1)
⇒ x+ 600 = 2000
⇒ x = 1400 dollars
⇒ Allen's original portion = 1400 dollars