Salut!
a) x + y + z = 24 ( 1 )
( x; y; z ) dp ( 3; 4; 5 )
[tex] \frac{x}{3} = \frac{y}{4} = \frac{z}{5} = k[/tex]
==> x = 3k
y = 4k
z = 5k
( 1 )
====> 3k + 4k + 5k = 24
12k = 24
k = 24 : 12
k = 2 ✓
x = 3 • 2
x = 6 ✓
y = 4 • 2
y = 8 ✓
z = 5 • 2
z = 10 ✓
b) x + y + z = 36 ( 1 )
( x; y; z ) dp ( 3; 4; 5 )
[tex] \frac{x}{3} = \frac{x}{4} = \frac{z}{5} = k[/tex]
==> x = 3k
y = 4k
z = 5k
( 1 )
====> 3k + 4k + 5k = 36
12k = 36
k = 36 : 12
k = 3 ✓
x = 3 • 3
x = 9 ✓
y = 4 • 3
y = 12 ✓
z = 5 • 3
z = 15 ✓
c) x + y + z = 132 ( 1 )
( x; y; z ) dp ( 3; 4; 5 )
[tex] \frac{x}{3} = \frac{y}{4} = \frac{z}{5} = k[/tex]
==> x = 3k
y = 4k
z = 5k
( 1 )
====> 3k + 4k + 5k = 132
12k = 132
k = 132 : 12
k = 11 ✓
x = 3 • 11
x = 33 ✓
y = 4 • 11
y = 44 ✓
z = 5 • 11
z = 55 ✓
