Let a,b,c,d,e be positive reals satisfying a + b = c a + b + c = d a + b + c + d = e If c=5, compute a + b + c + d + e .
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I like the trick you used..but i cant understand it.please explain it a little bit..
a + b = c [ a + b ] + c = d = > c + c = 2 c = d [ a + b ] + c + [ d ] = e = > c + c + 2 c = 4 c = e . : . [ a + b ] + c + [ d ] + [ e ] = x c + c + 2 c + 4 c = x = > 8 c = x w h e n c = 5 , x = 8 × 5 = 4 0
I went by a lengthy method. However,I think solution given by asker is more elegant. I went like this-
c=5
a+b=c
hence, a+b=5
a+b+c=d
hence, 5+5=d
a+b+c+d=e
hence, 5+5+10=e
hence,
a+b+c+d+e=5+5+10+20
\boxed{40}
I too did the same way.
a+b=c c=5 lets say a is 2 and b is 3 therefor c will be 5 and d is 10 if you add all of them together it will equal e e=20 20+2+3+5+10=40 therefor the answer is 40
Given: c = 5
a + b = c
a + b = 5
Given, a + b + c = d
( a + b ) + c = d
c + c = d
2 c = d
2 × 5 = d
d = 1 0
Given, ( a + b ) + c + d = e
5 + 5 + 1 0 = e
e = 2 0
Total sum: a + b + c + d + e = 5 + 5 + 1 0 + 2 0 = 4 0
Thus, the answer is: a + b + c + d + e = 4 0
C = 5
A + B = C
A + B = 5 or C = 5
A + B + C = D
C + C = D
5 + 5 = 10 or D = 10
A + B + C + D = E
D + D = E
10 + 10 = 20 or E = 20
A + B + C + D + E = E + E
A + B + C + D + E = 20 + 20
A + B + C + D + E = 40
C=5, a+b=c=5 A+b+c=5+5=10=d a+b+c+d=5+5+10=20=e a+b+c+d+e=5+5+10+20=40 The main answer is 40.
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a + b + c + d + e = 8 c = 8 ( 5 ) = 4 0