13. A number half of that number end one-third of that number are added. The result IS 22. What 15 the number

Mathematics

2 answers:

nordsb [41]3 years ago

6 0

X=is the number looked for.
x/2=is the half of "x".
x/3=is the one-third of the "x".
We suggest this equation:

x+(x/2)+(x/3)=22
Least common multiple=6
6x+3x+2x=132
11x=132
x=132/11=12

Te number is 12

To check:
A number (12)+ half of that number (6)+ the one-htird of that number(4) is:22

12+6+4=22

Alexxandr [17]3 years ago

5 0

Let the no. be x

x+x/2+x/3=22

6x+3x+2x/6=22

11x/6=22

11x=132

x=12

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zmey [24]

Answer:

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-Let y be the vertical distance from the eyes of the two men standing to the top of the clock tower.

#Taking the right triangle ACD:

$\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 60\textdegree=\frac{y+1.5}{x}\\\\y=x \ Tan \ 60\textdegree -1.5$

#Taking the right triangle ABD:

$\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 40\textdegree=\frac{y+1.5}{x+20}\\\\y=(x+20)\ Tan \ 40\textdegree -1.5$

#We equate the two yo solve for x and y;

$(x+20)\ Tan \ 40\textdegree -1.5=x\ Tan \ 60\textdegree -1.5\\\\(x+20)\ Tan \ 40\textdegree=x\ Tan \ 60\textdegree\\\\0.8391x+16.7820=1.7321x\\\\x=18.7939$