When you think Math is boring, think again. We can apply it everywhere, even on the things we thought they cannot be used. The mere reason that some people hate it does not mean it is no longer interesting. You just have to give it more time if you find it challenging.
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; you'll also love how it works once you keep practicing and solving 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, the answer 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:
A triangle's interior angle is 180 degrees
180= 2x + 4x + 6x
180 = 12x
15 = x
largest = 6x
6(15)
=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.
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:
The resulting figure will be a rectangle. Get first the measure of the sides of the square then add 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
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