Question

suma a 10 numere consecutive este 195 .determina numerele.

Answer 1

a+b+c+d+e+f+g+h+i+j=195
b=a+1
c=a+2
d=a+3
e=a+4
f=a+5
g=a+6
h=a+7
i=a+8
j=a+9

Prin segmente

a) |---|
b) |---|+1
c) |---|+2
d) |---|+3
e) |---|+4
f) |---|+5
g) |---|+6
h) |---|+7
i) |---|+8
j) |---|+9 } acolada la toate zece 195

1+2+3+4+5+6+7+8+9=45
195-45=150
au ramas zece segmente egale =>
150:10=15 ( acesta este a primul număr )
15+1=16 (b)
15+2=17 ( c)
15+3=18 (d)
15+4=19 (e)
15+5=20 (f)
15+6=21 (g)
15+7=22 (h)
15+8=23 (i)
15+9=24 (j)

PROBA
15+16+17+18+19+20+21+22+23+24=195 (adevărat )


a doua metodă

a+b+c+d+e+f+g+h+i+j=195
b=a+1
c=a+2
d=a+3
e=a+4
f=a+5
g=a+6
h=a+7
i=a+8
j=a+9

a+a+1+a+2+a+3+a+4+a+5+a+6+a+7+a+8+a+9=195
a×10 +45=195
a×10=195-45
a×10=150
a=150:10
a=15

b=15+1=16
c=15+2=17
d=15+3=18
e=15+4=19
f=15+5=20
g=15+6=21
h=15+7=22
i=15+8=23
j=15+9=24

Probă

15+16+17+18+19+20+21+22+23+24=195 (adevărat )