ALGEBRA EXPRESSIONS C2a

 

BANKING 1

 

Rayan deposited the amount of 20,000/= in a bank for 5 years and got a profit of 1500/=. Find the interest rate?

 

Solution

 

I = 1500/=, P = 20,000/=, T = 5 years, R = ?

 

I  = PRT

      100

 

1500  = 20000 x R x 5

                   100

 

1500  = 20000 x R x 5

                  100

 

1500  = 200 x R x 5

                      

1500  = 1000R

           

 ^1.51500  =   1000R

   1000       1000

 

 

Hence the interest rate was  1.5%

 

TRY THIS………….

 

Rayan deposited the amount of 6,000/= in a bank for 5 years and got a profit of 4200/=. Find the interest rate?

PROFIT AND LOSS K5

 

A man got a profit of 7400/= after selling an item. Find the buying price if the percentage profit was 10%.

 

Solution

 

%’ge profit = Profit   X  100    where B. P. represents Buying Price.

                         B.P

 

10% = 7400   X  100   

            B.P.

 

B.P. x 10% = 740,000   x B.P.  [multiplying by B.P. both sides]

                       B.P.

 

 

B.P. x 10 = 740,000   

 

        

B.P. x 10¹ =   740,000   

  ₁10                   10

 

B.P. =74,000

                      

Hence Buying Price was 74,000/=

 

TRY THIS………………

 

A man got a profit of 90,500/= after selling an item. Find the buying price if the percentage profit was 20%.

 

EXPONENTIALS C2a

 

9^x =3^x +72; find x

 

Solution

 

9^x =3^x +72

9^x - 3^x = 72    taking 3x on the left side

9^x - 3^x – 72 = 0.  Taking 72 on the left side as well

3^2x - 3^x – 72 = 0.   Rewriting 9^x as 3^2x.

(3^x)² – (3^x) – 72 = 0.   Factoring 3^x out.

      Let u = 3^x  ……… (i)

(u)² – (u) – 72 = 0.  

u² – 9u + 8u – 72 = 0   [Factorizing by splitting the middle term].

 

(u² – 9u) + (8u – 72) = 0  

u(u – 9) + 8(u – 9) =0

(u – 9)(u + 8) =0

 u – 9 = 0 or  u + 8  =0

u = 9 or  u =-8

 

We neglect the –ve answer and we stick with the positive one.

 

 Now from (i) u = 3^x 

9 = 3^x

3² = 3^x   equal bases they cancel out.

 

x = 2

 

TRY THIS………….

 

9^x =3^x + 11¹/₄; find x

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