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