6.
a) ( a + a : a - a : a ) × a = 81
( a + 1 - a : a ) × a = 81
( a + 1 - 1 ) × a = 81
( a + 0 ) × a = 81
a × a = 81 ⇒ a = 9
b) a × ( a × 0 + a : a + 0 : a ) = 17
a × ( 0 + a : a + 0 : a ) = 17
a × ( 0 + 1 + 0 : a ) = 17
a × ( 0 + 1 + 0 ) = 17
a × 1 = 17 ⇒ a = 17
7.
15 lazi ............ 24kg portocale
13 lazi ............. 18kg banane
29 lazi ............ 32kg mere
⇒ 15 lazi × 24kg portocale = 360kg portocale
⇒ 13 lazi × 18kg banane = 234kg banane
⇒ 29 lazi × 32kg mere = 928kg mere
T = portocale + banane + mere
T = 360kg + 234kg + 928kg = 1522kg fructe
8.
2 _ 8 _ 9 _ 3 = 19 ⇒ ( 2 × 8 ) + ( 9 : 3 ) = 19
2 _ 8 _ 9 _ 3 = 3 ⇒ ( 8 × 3 ) : 2 - 9 = 3
2 _ 8 _ 9 _ 3 = 7 ⇒ ( 2 + 8 ) - ( 9 : 3 ) = 7
9.
a = 105 × 5 + 2 × 105 = 105 × ( 5 + 2 ) =
a = 105 × 7 = 735
b = 203 × 4 + 203 × 0 = 203 × 4 + 0 = 812
c = 502 × 1 + 502 × 1 = 502 + 502 = 1004
⇒ 4 × a + 4 × b + 4 × c = 4 × ( a + b + c )
⇒ 4 × ( a + b + c ) = 4 × ( 735 + 812 + 1004)
⇒ 4 × ( 1547 + 1004 ) = 4 × 2551 = 10204
10.
17 ; 34 ; 51 ; 68 ; 85 ; ...
17 = 17 × 1
34 = 17 × 2
51 = 17 × 3
68 = 17 × 4
85 = 17 × 5
⇒ Observam ca șirul se repeta din 17 in 17 :
⇒ al 29-lea termen este : 29 × 17 = 493
⇒ al 129-lea termen este : 129 × 17 = 2193
