Tag: mental additions and subtractions

Let the number of 50 paise coins =x
So the number of 25 paise coins=2x
Amount with 50 paise coines=0.5x
Amount with 25 paise coines=0.5x
According to question 
0.5x+0.5x=27
Or x=27
So the number of 50 paise coins=x=27
Or the number of 25 paise coines=2x=54 

In the given Arithmetic Progression,
First term $ = a  = 1 $
Common difference $ = 5 - 1 = 4 $

Let $ 4n - 3 $ be the $  k $ th term.

Then $ {x} _{n} = a + (n-1)d $
$ => 4n- 3 = 1 + (k-1)4 $
$ => 4n -1 = 1 +4k-4 $
$ => k = n $

So,  $ 4n - 3 $ is the $ n $ th term.

Now, Sum to 'n' terms of an AP $ = \frac {n}{2} (2a+(n-1)d) = \frac {n}{2} (2+(n-1)4) = \frac {n}{2} (4n-2) =n(2n-1) $

Distance between two points $ ({x} _{1}, {y} _{1}) $ and $ ({x} _{2}, {y} _{2}) $ is $ \sqrt {{({x} _{2}-{x} _{1})}^{2} + {{(y} _{2}-{y} _{1})}^{2} } $

So, distance between $ (-4,-5) ; (-4,-10) $ is $ \sqrt {{(-4+4)}^{2} + {(-10+5)}^{2} } = 5 $

Given, $ 14y - 4 = 24y + 26 $
$ \Rightarrow  14y-24y = 26 + 4 $
$ \Rightarrow  -10y = 30 $
$ \Rightarrow  y = -3 $
Thus $ 12y = 12 \times (-3) = -36 $

• Grace has $8$ red , $4$ green , $4$ blue jellybeans
• In order to have one of each color , she should take out $7$ red, $3$ green , $3$ blue jellybeans
• So she has to take out $7+3+3=13$ jellybeans

Smallest three digit number $=100$

Greatest three digit number $=999$