A compilation of interesting math problems used in real life. This is the math that you need to see in order to see the usefulness of math and as a result appreciate math.
Investment. 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?
background knowledge: Percent and solving equations with fractions
Solution:
Let x be the part that is invested at 8%. The other part invested at 12% is 10000  x.
x ×
8
100
+

(10000  x) ×
12
100
=

10000 ×
11
100

8x
100
+

120000  12x
100
=

110000
100

100 ×
8x
100
+

100 ×
120000  12x
100
=

100 ×
110000
100

x ×
8
100
+

(10000  x) ×
12
100
=

10000 ×
11
100

8x
100
+

120000  12x
100
=

110000
100

100 ×
8x
100
+

100 ×
120000  12x
100
=

100 ×
110000
100

2500 should be invested at 8% and 7500 should be invested at 12%
Consumer Price Index. 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?
background knowledge: Ratio and proportion
Solution:
Let x be the monthly salary in 2015.
x
800
=

280
70

70
70
x

=
224000
70

x
800
=

280
70

70
70
x

=
224000
70

Business. 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?
background knowledge: System of linear equations
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
Ecology. 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?
background knowledge: Linear equation
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
Keep in mind though that about 1000 feet beneath the ocean, it is already very dangerous.
Demography. 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?
background knowledge: Multiplicative principle ( Counting )
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 09.
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
The counting principle says to multiply all the choices
Numbers of license plates = 25 × 25 × 25 × 25 × 10 × 10 = 39,062,500Therefore, there will be more than enough license plates.
The interesting math problems above were put here to show you how math is applied in real life. It is my hope that you will love math as you explore them. I will update this page with more and more interesting math problems. Keep coming back!
Supply and demand. Problem #6: Read problem
Background knowledge: Inverse variation, slopeintercept form, solve quadratic equations.
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