Question

Dividir o número 1 200 em duas partes diretamente proporcionais a:A) 2 e 4 B) 10 e 2C) 5 e 4 D) √24 e √6

Answer 1

A.-)
P1 = 2*X
P2 = 4*X

P1 + P2 = 1200
2X + 4X = 1200
6X = 1200
X = 1200/6
X = 200

P1 = 2*X
P1 = 2 * 200
P1 = 400


P2 = 4*X
P2 = 4 * 200
P2 = 800


B.-)
P1 = 10*X
P2 = 2*X

P1 + P2 = 1200
10*X + 2*X = 1200
12*X = 1200
X = 1200/12
X = 100

P1 = 2*X
P1 = 2*100
P1 = 200

P2 = 10*X
P2 = 10*100
P2 = 1000


C.-)
P1 = 5*X
P2 = 4*X

P1 + P2 = 1200
5*X + 4*X = 1200
9X = 1200
X = 1200/9..(÷3)
X = 400/3

P1 = 5*X
P1 5 * 400/3
P1 = 2000/3

P2 = 4*X
P2 = 4*400/3
P2 = 1600/3


D.-)
P1 = \|24*X
P2 = \|6*X

P1 + P2 = 1200
\|24*X + \|6*X = 1200
\|4x6*X + \|6*X = 1200
2*\|6*X + \|6*X = 1200
3*\|6 *X = 1200
X = 1200
.......____
........3*\|6

X = 400
.......___
........\|6

X = 400 x \|6
.......____....___
.........\|6.........\|6

X = 400*\|6
.......______..(÷2)
.............6

X = 200*\|6
........______
..............3

P1 = \|24 * X
P1 = \|4x6 * 200*\|6
....................________
............................3

P1 = 2\|6 * 200\|6
...................______
.........................3

P1 = 400 * 6
.........______
..............3

P1 = 400 * 2

P1 = 800


P2 = \|6 * X
P2 = \|6 * 200x\|6
.................._______
......................3


P2 = 200*\|6
.........______
................3