Question

In winter, the temperatures at a hill station from Monday to Friday are in A.P. The sum of the temperatures from Monday to Wednesday is $0$, while the sum of the temperatures on Thursday and Friday is ${15}^{\circ }$. Find the temperatures on each of the weekday.

Answer 1

Let the temperature from Monday to Friday as

Monday	Tuesday	Wednesday	Thursday	Friday
$a-2d$	$a-d$	$a$	$a+d$	$a+2d$

By the given condition sum of the temperature of Monday, Tuesday, Wednesday is zero
$\therefore$ $(a-2d)+(a-d)+a=0$
$3a-3d=\mathrm{0..........}\left(i\right)$
Also sum of the temperature of Thursday and Friday is $15$
$(a+d)+(a+2d)=15$
$2a+3d=\mathrm{15......}\left(ii\right)$
Adding equations $\left(i\right)$ and $\left(ii\right)$
$3a-3d=0$
$2a+3d=15$
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$\therefore$ $5a=15$
$\therefore$ $a=3$
Substituting $a=3$ in equation $\left(i\right)$
$3\left(3\right)-3d=0$
$9-3d=0$
$\therefore$ $-3d=-9$
$\therefore$ $3d=9$
$\therefore$ $d=3$
Monday $=a-2d=3-2\times 3=3-6=-3$
Tuesday $=a-d=3-3=0$
Wednesday $=a=3$
Thursday$=a+d=3+3=6$
Friday $=a+2d=3+2\times 3=3+6=9$
$\therefore$ Temperature of the five days are $-3,0,3,6$ and $9$ respectively.