Question

Sa se afle numerele x,y,z stiind ca sunt direct proportionale cu numerele 3,4,5 si a) x+y+z=84
b) x+2y+3z=52

Answer 1

(x, y, z) d.p. (3, 4, 5)
x/3 = y/4 = z/5 = k
x/3 = k => x = 3k
y/4 = k => y = 4k
z/5 = k => z = 5k
a) x + y + z = 84 => 3k + 4k + 5k = 84 => 12k = 84 => k = 84/12 => k = 7
x = 3k => x = 3 × 7 => x = 21
y = 4k => y = 4 × 7 => y = 28
z = 5k => z = 5 × 7 => z = 35
b) x + 2y + 3z = 52 => 3k + 2 × 4k + 3 × 5k = 52 => 3k + 8k + 15k = 52 => 26k = 52 => k = 52/26 => k = 2
x = 3k => x = 3 × 2 => x = 6
y = 4k => y = 4 × 2 => y = 8
z = 5k => z = 5 × 2 => z = 10

Answer 2

Răspuns

{x,y,z} DP {3,4,5}

=> x/3 = y/4 = z/5 = k (1)

A. x+y+z=84

(1) => x=3k

y=4k

z=5k

3k+4k+5k=84

12k=84

=> k=7

x=3k=3×7=21

y=4k=4×7=28

z=5k=5×7=35

B. x+2y+3z=52

(1) => x=3k

y=4k

z=5k

2y=2×4k=8k

3z=3×5k=15k

3k+8k+15k=52

26k=52

=> k=2

x=3k=3×2=6

2y=8k=8×2=16 => y=8

3z=15k=15×2=30 => z=10

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