45 new houses...
1/3 were sold......1/3(45) = 45/3 = 15 houses sold.....leaving 45 - 15 = 30 houses left. 1/5 of remaining houses sold....1/5(30) = 30/5 = 6...so 6 more houses were sold.....leaving 30 - 6 = 24 houses
24 houses are left <==
Step 1: Set up the synthetic division. ...
Step 2: Bring down the leading coefficient to the bottom row.
Step 3: Multiply c by the value just written on the bottom row. ...
Step 4: Add the column created in step 3.
If order matters, then there are 12 ways to do this
If order does not matter, then there are 6 ways to do this
===========================================
We have 4 choices for the first slot and 3 choices for the next (we can't reuse a letter) so that's where 4*3 = 12 comes from
If order doesn't matter, then something like AB is the same as BA. So we are doubly counting each possible combo. To fix this, we divide by 2: 12/2 = 6
To be more formal, you can use nPr and nCr to get 12 and 6 respectively (use n = 4 and r = 2)
Given that
(2/x)+(3/y) = 13--------(1)
(5/x)-(4/y) = -2 -------(2)
Put 1/x = a and 1/y = b then
2a + 3b = 13 ----------(3)
On multiplying with 5 then
10a +15 b = 65 -------(4)
and
5a -4b= -2 ----------(5)
On multiplying with 2 then
10 a - 8b = -4 -------(6)
On Subtracting (6) from (4) then
10a + 15b = 65
10a - 8b = -4
(-)
_____________
0 + 23 b = 69
______________
⇛ 23b = 69
⇛ b = 69/23
⇛ b =3
On Substituting the value of b in (5)
5a -4b= -2
⇛ 5a -4(3) = -2
⇛ 5a -12 = -2
⇛ 5a = -2+12
⇛ 5a = 10
⇛ a = 10/5
⇛ a = 2
Now we have
a = 2
⇛1/x = 2
⇛ x = 1/2
and
b = 3
⇛1/y = 3
⇛ y = 1/3
<u>Answer :-</u>The solution for the given problem is (1/2,1/3)
<u>Check</u>: If x = 1/2 and y = 1/3 then
LHS = (2/x)+(3/y)
= 2/(1/2)+3/(1/3)
= (2×2)+(3×3)
= 4+9
= 13
= RHS
LHS=RHS is true
and
LHS=(5/x)-(4/y)
⇛ 5/(1/2)- 4/(1/3)
⇛(5×2)-(4×3)
⇛ 10-12
⇛ -2
⇛RHS
LHS = RHS is true
