ALGEBRA - solved problems
Basic percent formulas
 29 What is 25% of 80?
 Solution: From the proportion,
part : base (whole) = rate : 100    or    y : x = p : 100
 then, , and we calculate, the part or amount  y, the rate p and the base value x
Since given,  x = 80,   p% = 25%,   y = ?
 Therefore, 30 What percent of 80 is 20?
 Solution: Given,    y = 20,   x = 80,   p% = ?
 Therefore, 31 What is the base value if  25% of it is 20?
 Solution: Given,    p% = p/100 = 25%,   y = 20,   x = ?
 Therefore, The base value therefore represents 1% of the base value.
Percent increase or decrease,  base (x), amount (y), percent (p)
 32 In the price of \$33 included is tax of 10%.  What is net price?
 Solution: From the proportion,
 x : 100 = ( x ± y ) : ( 100 ± p) then, y : p = ( x ± y ) : ( 100 ± p)
where   x ±   denotes original or base value x increased or decreased by amount y
 then, , and Since given,  x y = 33 ,   p% = 10%,   x = ?
 Therefore, 33 Price reduced by 20% amounts to \$320. How much is reduced?
Solution:    Given,  x -  y = 320 ,   p% = 20%,   y = ?
 Therefore, Interest calculations
Simple interest
 34 Somebody deposits \$20,000 into a savings account where the rate of interest is 4.8% annually.
How much money in interest will earn after nine months?
An amount of money deposited into a bank for a given period of time brings to the depositor a
profit called interest
The amount of interest (I ) the bank pays you, depends on the interest rate ( i % ), the amount of money
deposited, denoted as principal P also called original balance (or initial investment), and the period of time n
the money is deposited,
 since    P : 1 = I : (i · n)    then, Therefore, , and Solution:   Given,  P = \$20000 ,   p% = 4.8%  and  n = 9 months,  I = ? 35 A bank lends a company money for the six months period at a rate of  8% annually.
How much was lent if the company should pay \$12,000 of interest?
Solution:   Given,  I = \$12000 ,   p% = 8%  and  n = 6 months,  P = ? 36 At what an interest rate was borrowed \$75,000 for one year if \$3,000 to interest is charged?
Solution:   Given,  P = \$75000 ,   I = \$3000  and  n = 1 year,  i = ? 37 For what period of time should be deposited \$200,000 at a 6% interest rate to earn \$6,000
of interest?
Solution:   Given,  P = \$200,000 ,  p% = 6%  and  I = \$6,000,  n = ?    Solved problems contents