Proving Mathematics is Basic? Sample Problems and their Solutions, Explained!

When others think Mathematics is boring, don't just say they should need to think again. It's a case-to-case basis as we have our own preferences and favorites.

However, think of something based on what you can see from your surroundings. Even on the things we thought it cannot be used, there is Math behind it, right? The buildings that were built and the ongoing constructions, the natural things we see, the clothes we wear, there is Math behind them.

Forget the boring notion and welcome positivity as we're going to unveil what makes this subject amazing and interesting.

In this article, we are not just merely solving basic math problems. We are also building a foundation that will help you in loving it. As they say, just because you don't like something does not mean they're no longer necessary to you. They are more than essential. Once you learn something, you'll also love how it works once you keep practicing and solving them.

Main Points

Math can be challenging but with the right mindset and discipline, it can be learned.

Knowing the four fundamental operations of Mathematics is very important and should be mastered or at least learned.

Math can be found everywhere. Be it the shirt or pants we currently wear to complex calculations in building towers, it is really significant and useful.

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Sample Math Problems and How to Solve Them

1. What is the answer to 100 – 99 + 98 – 97 + 96 – 95 + … + 2 – 1?

Solution:
100 – 99 + 98 – 97 + 96 – 95 + … + 2 – 1
(100-99) + (98-97) + (96-95) + ... + (2-1)
1 + 1 + 1 + ... + 1
=50 

If you have noticed, every two adjacent number has a difference of 1. Therefore, divide the total number by 2. You will get the answer which is 50.

2. When 30 is divided by x, the quotient is 7 and the remainder is 2. What is x?

Solution:
30 ÷ x = 7, r=2
30 = 7x + 2

Combine similar terms. Note that if you transfer a term on the other side, its sign will be changed to its opposite.

30 - 2 = 7x
28 = 7x
4 = x

3. In our barangay, 25% of the girls play volleyball. There are 200 girls in our barangay. How many of them do not play volleyball?

Solution:
100% - 25% = 75%
200 x .75 = 150

Just get the percentage of those who will not play by getting the difference of 100% and the percentage of those who will play.

4. A triangle has sides of length 9 cm, 11 cm, and 16 cm. An equilateral triangle has the same perimeter. What is the length of each side of the equilateral triangle?

Solution:
9 + 11 + 16
36

Since the length of each side of an equilateral triangle is being asked, just divide it by 3.
36 ÷ 3 = 12

5. The degree measure of the angles of a triangle are in the ratio 2 ∶ 4 ∶ 6. What is the measure of the largest?

Solution:
180= 2x + 4x + 6x
180 = 12x
15 = x
largest = 6x
6(15)
=90 degrees

If you are wondering about how I came up with 180 degrees, remember that a triangle's interior angle is 180 degrees. To get it, deduct 1 from the total number of sides and then multiply it to 90 degrees.

6. The sum of 44.54 and x is 65.255, find x.

Solution:
65.255 = 44.54 + x
65.255 - 44.54 = x
20.715 = x

7. The product of 45 and y is 855, find y.

Solution:
855 = 45y

Divide both sides by 45
19 = y

8. Three integers in the ratio of 2:4:6 has a sum of 642, what is the smallest integer?

Solution:
642 = 2x + 4x + 6x
642 = 12x
53.5 = x
smallest integer = 2(x)
2(53.5)
=107

9. Two squares each with a perimeter of 8 cm are placed side by side. What is the perimeter of the resulting figure?

Solution:

Putting two squares side by side, the resulting figure will be a rectangle. Get first the measure of the sides of the square then adds the new sides together.

8 ÷ 4
w = 2
2 + 2
l = 4

Now get the new perimeter
2l + 2w
2(4) + 2(2)
8 + 4
=12 cm

10. Barbie bought a doll that was discounted 20%. If she saved Php15.00, what was the original price of the doll?

Solution:
.20x = 15

Divide both sides by 20
x = 75
Php 75

11. A wire 80 cm in length is cut into two parts in the ratio 3 ∶ 1. Each part is bent to form a square. What is the total area of the two squares?

Solution:
80 = 3x + x
80 = 4x
20 = x

First Square
3(x)
3(20)

Perimeter = 60
Area = (60/4) (60/4)
(15)(15)
= 225 square cm

Second Square
1(x)
1(20)

Perimeter = 20
Area = (20/4) (20/4)
(5)(5)
= 25 square cm
Total area = 225 + 25
= 250 square cm

12. If you can read 1.5 pages per minute, how many pages can you read in 3 hours?

Solution:
1.5 x 3 x 60
= 270 pages

13. Allan buys oranges at Php25.00 for 3 pieces and plans to sell them at Php45.00 for 5 pieces. How many oranges must he sell in order to make a profit of Php200.00?

Solution: 
Cost per orange for 3 for Php25:  
Php25 ÷ 3 = Php8.333

Selling price per orange at 5 for Php45:
Php45 ÷ 5 = Php9

Profit = Selling Price - Cost
Profit = Php9 - 8.333
Profit = Php0.667 per orange

Profit function
f(x) = 0.667x  
Where:
x = number of oranges
f(x) = total profit

Find x, the total number of oranges to gain a profit of Php200.00:
200 = 0.667x
200/0.667 = 0.667x/0.667
x = 299.850
x ≈ 300 oranges

14. By how much is 7/4 greater than 5/6?

Solution:
7/4 - 5/6
21/12 - 10/12
11/12

15. Nine is what percent of 45?

Solution:
9 = 45x
.20 = x
x = 20%

16. I am thinking of a number. If I add 48 and subtract 27, I get 35. What is the number?

Solution:
x + 48 - 27 = 35
x = 35 + 27 - 48
x= 14

17. A book which costs 875 is sold for a 20% discount. How much is the book’s discounted price?

Solution:
875 x .20
=175
875 - 175
=Php 700

18. The length of the rectangle is 3 more than its width. Its perimeter is 48 centimeters. What length?

Solution:
3 + 2x + 2x = 48
3 + 4x = 48
4x = 48 - 3
4x = 45
x = 11.25
2x + 3
2(11.25) + 3
22.50 + 3
=25.50 cm 

19. Joy received Php500 from his uncle and Php200 from her aunt. She spent Php150 in buying school supplies and Php120 for lunch. How much money she has left?

Solution:
Php 500 + Php 200
=Php700
Php 150 + Php 120
=Php 270
Php 700 - Php 270
=Php 430

20. Cindy spent 126 pesos for buying notebooks. Each notebook costs 14 pesos. How many notebooks did she buy?

Solution:
14x = 126
x= 126/14
x= 9
= 9 notebooks

A few things to remember

It may cause headache to some, but overall, Mathematics contributes help to small and huge projects. As we observe from above samples, no matter how complex they are, the solutions made them look like easy to answer and that's what we can realize as well.

Instead of giving up and cursing it, try to look at the bigger picture. Some problems written vaguely may seem complex, but in reality, it's easy to spot the formula to be used.

It is not only about calculating. You need to memorize as well, especially the formulas and important terms. But do not just rely on reading the concept. You must apply it also though practice solving.

Once you develop a habit of reading and solving math questions, you'll see improvement in your next exam. Just don't be harsh to yourself because I believe that you can get it and you can ace it.