An algebra problem by Israel Sapnu Jr.

Algebra Level 1

Solve for x in the equation x+2(x+1)+3(x+1)+...+10(x+1)=110.


The answer is 1.018.

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2 solutions

Omkar Kulkarni
Feb 3, 2015

x + 2 ( x + 1 ) + 3 ( x + 1 ) + . . . + 10 ( x + 1 ) = 110 x+2(x+1)+3(x+1)+...+10(x+1)=110

( x + 1 ) + 2 ( x + 1 ) + 3 ( x + 1 ) + . . . + 10 ( x + 1 ) = 111 (x+1)+2(x+1)+3(x+1)+...+10(x+1)=111

( x + 1 ) ( 1 + 2 + 3 + . . . + 10 ) = 111 (x+1)(1+2+3+...+10)=111

55 ( x + 1 ) = 111 55(x+1)=111

x + 1 = 111 55 x+1=\frac{111}{55}

x = 111 55 1 x=\frac{111}{55}-1

x = 56 55 1.018 x=\frac{56}{55}\approx\boxed{1.018}

Lu Chee Ket
Feb 3, 2015

(x + 1)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) = 110 + 1

(x + 1) 55 = 111

x = 111/ 55 - 1 = 1.0181818181818181818181818181818

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