Most Searched Math Problems With Solutions

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MY ASSIGNME NT SE R VICE S
COOL MATH PROBLEMS
Presented by MITCHELL LEE
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Problem 1 An investor with 10000 invests part
of the money at 8 and the rest at 12. How much
should be invested at each rate to yield 11 of
the total amount? Solution Let x be the part
that is invested at 8. The other part invested
at 12 is 10000 - x. x 8 (10000 - x) 12
10000 11 x 8/100 (10000 - x) 12/100
10000 11/100 8x/100 120000 - 12x/100
110000/100 Multiply both sides by 100 100
8x/100 100 120000 - 12x/100 100 110000/100
We get 8x 120000 - 12x 110000 12x - 8x
120000 - 110000 4x 10000 x 2500 since 4
2500 10000
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Problem 2 Suppose in 1960, the consumer price
index was 70

• while in 2015 it is 280. What monthly salary in
  2015 would have the same purchasing power as a
  monthly salary of 800 dollars in 1960?
• Solution Let x be the monthly salary in 2015.
  x/800 280/70
• x 70 280 800
• 70x 224000
• 70/70 x 224000/70 x 3200

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Problem 3 A bookstore made 11000 dollars
selling 3000 math
books and 1000 physics books. A customer bought 1
math book and 1 physics book and paid 7 dollars.
What is the price of each book? Solution Let x
be the price of the math book and y be the price
of the physics book x y 7 3000 x 1000
y 11000 Use x y 7 to solve for y x - x y
7 - x y 7 - x Substitute 7 - x for y in 3000
x 1000 y 11000 3000 x 1000 (7 - x)
11000 2000x 4000 x 2 since 2000 2
4000 Since 2 5 7, y 5 The price of a math
book is 2 dollars and the price of a physics book
is 5 dollars.
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Problem 4 The pressure someone experiences as
he or she dives
deeper and deeper in the ocean increases
linearly. On the surface, the pressure is close
to 15 pounds per square inch. 33 feet below the
surface, the pressure is 30 pounds. If 25000
pounds per sq inch can crush your bones, what
depth is extremely dangerous for
humans? Solution First, model the pressure ( p )
in terms of depth ( d ) with a linear
equation. We will find the equation p md b
Use (0, 15) and (33, 30) to find m m 30 - 15/33
- 0 m 15/33 0.45 p 0.45d b Use (0, 15)
to find b 15 0.45 0 b p 0.45d 15 25000
- 15 0.45d 15 - 15 d 24985/0.45 55522
feet
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Problem 5 The population in the state of
Florida right now is 19.9
million. The latest format for passenger plates
in the state of Florida is AAA A00 through ZZZ
Z99. If the letter o cannot be used when making
plates, will the state have enough license plate
numbers for its residents? Solution The format
shows that the first 4 characters are letters and
the last 2 characters are numbers. There are 26
characters in the Enlgish alphabet. Since the
letter o cannot be used, the choice is now 25.
There are 10 characters for the numbers 0-
9. Notice also that numbers or letters can be
repeated! For the first letter, there are 25
choices For the second letter, there are 25
choices For the third letter, there are 25
choices For the fourth letter, there are 25
choices For the first number, there are 10
choices For the second number, there are 10
choices Numbers of license plates 25 25 25
25 10 10 39,062,500 Therefore, there
will be more than enough license plates.
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