Ten ten

Algebra Level 1

Evaluate 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 . \frac { 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 } { 1 + 2 + 3 + 4 +5+6+7+8+9+10}.


The answer is 5.

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21 solutions

Alexander Sludds
Dec 15, 2013

Factoring a 5 5 out of the top we see that we have 5 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 5*\frac{1+2+3+4+5+6+7+8+9+10}{1+2+3+4+5+6+7+8+9+10} . This simplifies to 5 5

nice..

Røhít Mähtø - 7 years, 5 months ago

5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 5 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 ) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 5 \frac{5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50}{1+2+3+4+5+6+7+8+9+10} = \frac{5 (1+2+3+4+5+6+7+8+9+10)}{1+2+3+4+5+6+7+8+9+10} = 5

5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 \frac{5+10+15+20+25+30+35+40+45+50}{1+2+3+4+5+6+7+8+9+10} = 5 × ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 ) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 =\frac{5 \times(1+2+3+4+5+6+7+8+9+10)}{1+2+3+4+5+6+7+8+9+10} = 5 =\boxed{5} Therefore, the answer is 5 \boxed{5} .

Vanitha Ma
Dec 15, 2013

The sum of n terms in arithmetic progression is s_n=1/2 n(a+l) where n=number of terms a=initial value and l=final value =(1/2 10(5+50))/(1/2 10(1+10)) =(10(55))/(10(11)) =5

Sunil Pradhan
Dec 15, 2013

(5+10+15+20+25+30+35+40+45+50)/(1+2+3+4+5+6+7+8+9+10) = 5(1+2+3+4+5+6+7+8+9+10)/(1+2+3+4+5+6+7+8+9+10) . = 5

Jordi Bosch
Dec 15, 2013

The numerator can be written as 5 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 ) 5(1+2+3+4+5+6+7+8+9+10) Simplify with the denominator and you get 5 \boxed{5}

Oli Hohman
Mar 3, 2015

One arithmetic sequence divided by another. Use arithmetic sum formula (n*(a 1+a n)/2 or simply factor 5 out of the numerator.

Pappu Ebilish
Apr 5, 2014

(1/2 10(5+50))/(1/2 10(1+10)) =(10(55))/(10(11)) =5

Anirban Mondal
Jan 19, 2014

firstly,(5+50)+(10+45)+............+(25+30)=(55x5) , secondly,(1+10)+(2+9)+........+(5+6)=11x5 then,(55x5)/(11x5)=5....answer..

Ramlakhan Yadav
Dec 18, 2013

(5+10+15+20+25+30+35+40+45+50)/(1+2+3+4+5+6+7+8+9+10)=5.(1+2+3+4+5+6+7+8+9+10)/(1+2+3+4+5+6+7+8+9+10)=5

Naveenkumar Nani
Dec 17, 2013

275/45=5

Michael Gaul
Dec 16, 2013

You could add up all the numbers that are on the numerator and get 295.Then divide the sum of the denominator which is 55. However, you could figure out the two middle numbers' on the numerator's sum which is 55 (25+30).Then divide the 55 by the middle numbers' total which is 11 (5+6). The answer you will then get is 5

Ritesh Surve
Dec 16, 2013

TAKE 5 common...easy!

Prasun Biswas
Dec 16, 2013

5 + 10 + 15 + . . . + 50 1 + 2 + 3 + . . . + 10 = 5 ( 1 + 2 + 3 + . . . + 10 ) ( 1 + 2 + 3 + . . . + 10 ) = 5 \frac{5+10+15+...+50}{1+2+3+...+10} = \frac{5(1+2+3+...+10)}{(1+2+3+...+10)} = 5

(5+10+15+20+25+30+35+40+45+50)/5 = 5(1+2+3+4+5+6+7+8+9+10)/(1+2+3+4+5+6+7+8+9+10) = [5(55)]/55 = 5

Arafat Asim Riyad
Dec 16, 2013

5(1+2+3+4+5+6+7+8+9+10),then ans is 5

Anubhav Singh
Dec 16, 2013

10/2 (5+50)/[10 11/2)=5*55/55=5 and one thing mre pls bring back old brillliant

Shine Max
Dec 16, 2013

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

I know the answer but tell answer to others in a simple way

akshringi shringi - 7 years, 5 months ago

take 5 common from all the terms from the numerator.. u will get the denominator so both will cancel and u will get the common 5 as the answer.

Nishant Tyagi
Dec 15, 2013

take 5 common from the numerator equation becomes

5(1+2+3+4+5+6+7+8+9+10)/(1+2+3+4+5+6+7+8+9+10)

hence answer is 5

Hùng Minh
Dec 15, 2013

5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 = 5 x (1+ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10). So result is 5

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