Explicație pas cu pas:
11)
prima : x
a doua : y
a treia : z
x + y + z = 63
x = 2y
z = 3 + (x + y)
z = 3 + (2y + y)
z = 3 + 3y
2y + y + 3 + 3y = 63
6y + 3 = 63
6y = 63 - 3
6y = 60
y = 10
x = 2 × 10
x = 20
z = 3 + 3 × 10
z = 3 + 30
z = 33
12)
[tex] \frac{x}{y} = 1[/tex]
[tex] \frac{y}{z} = 2[/tex]
y - z = 4 => y = 4 + z
[tex] \frac{y}{z} = \frac{2}{1} [/tex]
[tex] \frac{4 + z}{z} = \frac{2}{1} [/tex]
[tex]4 + z = 2z[/tex]
4 = - z + 2z
4 = 2z - z
4 = z
y = 4 + z
y = 4 + 4
y = 8
[tex] \frac{x}{y} = 1[/tex]
[tex] \frac{x}{8} = \frac{1}{1} [/tex]
x = 8
13)
a + b + c = 100
a - x = 20 => a - 20 = x
b - x = 40
c - x = 10
b - (a - 20) = 40
b - a + 20 = 40
b - a = 40 - 20
b - a = 20 => b - 20 = a
c - (a - 20) = 10
c - (b - 20 - 20) = 10
c - (b - 40) = 10
c - b + 40 = 10
c - b = 10 - 40
c - b = - 30 => c + 30 = b
a = c + 30 - 20
a = c + 10
c + 10 + c + 30 + c = 100
3c + 40 = 100
3c = 100 - 40
3c = 60
c = 20
a = 20 + 10
a = 30
b = 20 + 30
b = 50
14)
x + y + z = 72
x - a = 9 => x - 9 = a
y - a = 6
z - a = 18
y - (x - 9) = 6
y - x + 9 = 6
y - x = 6 - 9
y - x = - 3 => y + 3 = x
z - (x - 9) = 18
z - x + 9 = 18
z - x = 18 - 9
z - x = 9
z - (y + 3) = 9
z - y - 3 = 9
z - y = 9 + 3
z - y = 12 => z - 12 = y
a = y + 3 - 9
a = y - 6
a = z - 12 - 6
a = z - 18
x = z - 12 + 3
x = z - 9
z - 9 + z - 12 + z = 72
3z - 21 = 72
3z = 72 + 21
3z = 93
z = 31
x = 31 - 9
x = 22
y = 31 - 12
y = 19
15)
bluza rosie : r
bluza verde : v
bluza galbena : g
r + v + g = 87
r = 2v
[tex]g = \frac{r}{2} - 5[/tex]
[tex]g = \frac{2v}{2} - 5[/tex]
[tex]g = v - 5[/tex]
2v + v + v - 5 = 87
4v - 5 = 87
4v = 87 + 5
4v = 92
v = 23
r = 2 × 23
r = 46
g = 23 - 5
g = 18
