Word Problems Using Percents
and Perimeter
By Dr. Carol A. Marinas
Is’s and Of’s
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What % is a of b?
x= a
100
b
The Pattern is:
% = “is”
100
“of”
Examples of Is/Of % Questions
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What number is
16% of 70?
16 = x
100 70
Cross multiply
16(70) = 100x
1120 = 100x
11.2 = x
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The number 45 is
25% of what
number?
25 = 45
100
x
Cross multiply
25x = 45(100)
25x = 4500
x = 180
Examples of Is/Of % Questions
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Find 23% of 20.
23 = x
100 20
Cross multiply
23(20) = 100x
460 = 100x
4.6 = x
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The number 42 is
what percent of 35?
x = 42
100 35
Cross multiply
35x = 42(100)
35x = 4200
x = 120
120 %
Word Problem - Sale Price
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Dillard’s advertised a 25% off sale.
If a London Fog coat originally
sold for $156, find the decrease
and the sale price.
Decrease .25(156) = 39 dollars
Sale price 156 - 39 = 117 dollars
Word Problems - Increased Price
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Time Saver increased the price of
a $.75 cola by 15%. Find the
increase and the new price.
Increase .15(.75) = .11
New price .75 + .11 = .86
Word Problem - Interest #1
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Zoya invested part of her $25,000 advance
at 8% annual simple interest and the rest at
9% annual simple interest. If her total
yearly interest from both accounts was
$2135, find the amount invested at each
rate.
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Explanation: $25,000 partly invested at 8% and
the rest at 9%. The total interest from these
investments is $2135. We are going to organize
the information in a table. We will need the
business formula: Principal*Rate=Interest
Word Problem - Interest (cont.)
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Put % rates as decimals in the Rate column. Put
the total principal of $25,000 and total interest of
$2135 in the bottom row. Put x in the principal row
for 8% so then 25000-x must be the principal
invested at 9%. Since Principal*rate=Interest
multiply the top 2 rows across. Your equation
comes from adding down the last column.
.08x + .09(25000-x) = 2135
.08x + 2250 - .09x = 2135
Principal
Rate
Interest
x
25000 - x
.08
.09
.08 x
.09 (25000 - x)
25000
2135
-.01x + 2250 = 2135
So x = $11500 @ 8%
-.01x = -115
25000-11500 = $13500 @ 9%
Word Problem - Interest #2
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Bruce invested a sum of money at 10%
annual simple interest and invested
twice that amount at 12% annual simple
interest. If his total yearly income from
both investments was $2890, how much
was invested at each rate?
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Explanation: x amount invested at 10%
and 2x amount invested at 12%. Complete
the table.
Word Problem - Interest #2
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Principal
Rate
Interest
x
2x
.10
.12
.10x
.12(2x)
2890
Multiply across the top 2 rows. The equation is
adding down the last column.
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.10x + .12(2x) = 2890
.10x + .24x = 2890
.34x = 2890
x = $8500 @ 10% and $17000 @ 12 %
Word Problems - Perimeter #1
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If the length of a rectangular parking lot is 10
meters less than twice its width, and the
perimeter is 400 meters, find the length of the
parking lot.
If x is the width, then 2x - 10 is the length. Perimeter
is distance around.
P= 2L + 2W
400 = 2(2x - 10) + 2(x)
400 = 6x - 20
420 = 6x So x = 70 meters (width) and
2(70) - 10 = 130 meters (length)
Word Problem - Perimeter #2
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A flower bed is in the shape of a triangle with one
side twice the length of the shortest side, and the
third side is 30 feet more than the length of the
shortest side. Find the dimension if the perimeter
is 102 feet.
If x is the shortest side, the second side is 2x, and
the third side is x + 30. The perimeter is the
distance around the triangular flower bed.
x + 2x + (x + 30) = 102
4x + 30 = 102
4x = 72 So x = 18 feet (shortest side); 2x = 36
feet (second side); x + 30 = 48 feet (third side)
The End !
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Remember word problems are difficult.
Some hints to help:
– You must first understand the problem
– Then assign x to your missing number
– Come up with a strategy. Write an
equation.
– Solve the equation.
– Check answer.
– Write solution including UNITS.