Math Word Problems Reviewer (Professional)

Reviewer's Note: Translate the words into a mathematical "sentence" one piece at a time. Words like "is" usually mean =, and "of" usually mean ×. Identifying what $x$ represents is half the battle.

Word problems translate real-life situations into mathematical equations. Success in this section requires both reading comprehension and mathematical skill.

Sa madaling salita: Isalin ang kwento sa math equation. Ang "is" ay laging =, at ang "of" ay laging ×.

Common Types of Word Problems

There are several recurring themes in Civil Service Exam word problems. Mastering these specific types will give you a significant advantage.

1. Age Problems

These involve finding the current or future age of individuals.

Strategy: Use "x" for the unknown age and set up an equation.
Example: "A father is 3 times as old as his son. In 10 years, he will be twice as old as his son. How old is the son now?"
- Son = $x$ , Father = $3x$
- In 10 years: $(3x + 10) = 2(x + 10)$
- $3x + 10 = 2x + 20 \implies x = 10$ . (The son is 10).
- Hack (Ibig sabihin): Kung ang anak ay $x$ , ang tatay ay $3x$ . Pagkalipas ng 10 taon, pareho silang madadagdagan ng 10. Ang tatay ( $3x+10$ ) ay magiging doble ( $2 \times$ ) ng anak ( $x+10$ ).

2. Work Problems

These involve multiple people or machines completing a task together.

Formula: $\frac{1}{t_1} + \frac{1}{t_2} = \frac{1}{t_{total}}$
Example: "Person A can paint a room in 4 hours. Person B can do it in 6 hours. How long will it take if they work together?"
- $\frac{1}{4} + \frac{1}{6} = \frac{1}{x}$
- $\frac{3 + 2}{12} = \frac{1}{x} \implies \frac{5}{12} = \frac{1}{x} \implies x = \frac{12}{5} = 2.4$ hours.
- Hack (Ibig sabihin): Ito ay para sa pagkuha ng bilis ng trabaho kapag nagtulungan. Gamitin ang fraction ng oras ng bawat isa.

3. Rate, Time, and Distance

These problems deal with moving objects and their speed.

Formula: Distance = Rate × Time ( $D = R \times T$ )
Example: "A car travels at 60 km/h for 3.5 hours. How far did it go?"
- $60 \times 3.5 = 210$ km.
- Hack (Ibig sabihin): I-multiply ang bilis sa tagal ng biyahe para makuha ang layo.

4. Averages (Mean)

Averages are used to find a central value for a set of data.

Formula: Average = Sum of items / Number of items
Example: "A student's grades are 85, 90, and 80. What is the average?"
- $(85 + 90 + 80) / 3 = 255 / 3 = 85$ .
- Hack (Ibig sabihin): I-add lahat ng values at i-divide kung ilan sila.

5. Ratio and Proportion

Ratios compare two quantities, while proportions show that two ratios are equal.

Example: "The ratio of boys to girls is 3:2. If there are 30 boys, how many girls are there?"
- $\frac{3}{2} = \frac{30}{x} \implies 3x = 60 \implies x = 20$ .
- Hack (Ibig sabihin): Pag-tapatin ang ratio at ang actual numbers gamit ang fraction.

Strategy for Solving

To excel in word problems, follow a systematic approach for every question.

Read carefully: Understand what is being asked. (Basahin nang mabuti.)
Identify the variables: Assign a letter (like $x$ ) to the unknown value. (Lagyan ng variable ang hinahanap.)
Translate into an equation: Turn the words into numbers and symbols. (Gawing math equation ang kwento.)
Solve the equation: Use basic algebra. (I-solve ang equation.)
Check your answer: Does the answer make sense? (I-check kung tama ang sagot.)

Practice Questions

A shirt is on sale for 25% off. If the original price was P800, what is the new price?
- A. P600
- B. P200
- C. P700
- D. P550
- Answer: A (P600).
- Hack (Ibig sabihin): Kunin ang 25% ng 800 ( $0.25 \times 800 = 200$ ). Ito ang bawas (discount). So, $800 - 200 = 600$ .
The sum of three consecutive integers is 45. What is the smallest integer?
- A. 13
- B. 14
- C. 15
- D. 16
- Answer: B (14).
- Hack (Ibig sabihin): Consecutive means magkakasunod ( $x, x+1, x+2$ ). Ang equation ay $3x + 3 = 45$ . So $3x = 42$ , $x = 14$ . Ang tatlong numero ay 14, 15, at 16.
A tank can be filled by Pipe A in 5 hours and emptied by Pipe B in 10 hours. If both are open, how long to fill the tank?
- A. 5 hours
- B. 7.5 hours
- C. 10 hours
- D. 15 hours
- Answer: C (10 hours).
- Hack (Ibig sabihin): Kapag may "emptied", subtract ang rate nito. $\frac{1}{5} - \frac{1}{10} = \frac{1}{10}$ . So $x = 10$ .
A car travels 120 km in 2 hours. What is its average speed in km/h?
- A. 50 km/h
- B. 60 km/h
- C. 65 km/h
- D. 70 km/h
- Answer: B (60 km/h).
- Hack (Ibig sabihin): Speed = Distance / Time. $120 / 2 = 60$ .
The average of four numbers is 25. If three of the numbers are 20, 22, and 28, what is the fourth number?
- A. 30
- B. 35
- C. 25
- D. 32
- Answer: A (30).
- Hack (Ibig sabihin): Ang total sum dapat ay $25 \times 4 = 100$ . I-add ang tatlo: $20+22+28 = 70$ . Ang kulang para maging 100 ay 30.
Maria is twice as old as her brother. In 5 years, the sum of their ages will be 25. How old is Maria now?
- A. 8 years old
- B. 10 years old
- C. 12 years old
- D. 14 years old
- Answer: B (10 years old).
- Hack (Ibig sabihin): Brother = $x$ , Maria = $2x$ . In 5 years: $(x+5) + (2x+5) = 25 \implies 3x+10 = 25$ . So $3x = 15$ , $x = 5$ (Brother). Maria is $2 \times 5 = 10$ .
If 5 workers can build a wall in 12 days, how many days will it take 3 workers to build the same wall?
- A. 15 days
- B. 18 days
- C. 20 days
- D. 24 days
- Answer: C (20 days).
- Hack (Ibig sabihin): Inverse Proportion. Mas konting tao, mas matagal matapos. $5 \times 12 = 3 \times x \implies 60 = 3x$ , so $x = 20$ .
A recipe for cookies requires 2 cups of flour to make 24 cookies. How many cups of flour are needed to make 60 cookies?
- A. 4 cups
- B. 5 cups
- C. 6 cups
- D. 7 cups
- Answer: B (5 cups).
- Hack (Ibig sabihin): Direct Proportion. $2/24 = x/60$ . Cross multiply: $120 = 24x$ , so $x = 5$ .
Two trains start from the same point and travel in opposite directions. One train travels at 80 km/h and the other at 100 km/h. After how many hours will they be 540 km apart?
- A. 2.5 hours
- B. 3 hours
- C. 3.5 hours
- D. 4 hours
- Answer: B (3 hours).
- Hack (Ibig sabihin): Dahil opposite directions, i-add ang speed ( $80+100 = 180$ km/h). $540 / 180 = 3$ .
A class has 40 students. If 60% are girls, how many boys are in the class?
- A. 16
- B. 20
- C. 24
- D. 30
- Answer: A (16).
- Hack (Ibig sabihin): Kung 60% ang girls, 40% ang boys. $0.40 \times 40 = 16$ .
John's monthly salary is P25,000. He spends 30% on rent, 20% on food, and saves the rest. How much does he save per month?
- A. P10,000
- B. P12,500
- C. P15,000
- D. P17,500
- Answer: B (P12,500).
- Hack (Ibig sabihin): Ang nagastos ay $30\% + 20\% = 50\%$ . So 50% din ang natira (savings). $0.50 \times 25,000 = 12,500$ .
The perimeter of a rectangle is 34 meters. If the length is 10 meters, what is the width?
- A. 7 meters
- B. 8 meters
- C. 9 meters
- D. 12 meters
- Answer: A (7 meters).
- Hack (Ibig sabihin): Perimeter = $2 \times (Length + Width)$ . $34 = 2 \times (10 + W) \implies 17 = 10 + W$ . So $W = 7$ .
A machine can produce 150 items in 6 minutes. How many items can it produce in 20 minutes?
- A. 400
- B. 450
- C. 500
- D. 600
- Answer: C (500).
- Hack (Ibig sabihin): Alamin muna ilan ang nagagawa sa 1 minuto ( $150 / 6 = 25$ items/min). Sa loob ng 20 mins: $25 \times 20 = 500$ .
Anna is 5 years older than Beth. The sum of their ages is 31. How old is Beth?
- A. 10
- B. 13
- C. 16
- D. 18
- Answer: B (13).
- Hack (Ibig sabihin): Beth = $x$ , Anna = $x+5$ . $x + x+5 = 31 \implies 2x = 26$ , $x = 13$ .
A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of picking a blue ball at random?
- A. 3/10
- B. 1/3
- C. 1/5
- D. 2/5
- Answer: A (3/10).
- Hack (Ibig sabihin): Probability = (Blue balls) / (Total balls). Total ay $5+3+2 = 10$ . So $3/10$ .
If you can buy 4 apples for P60, how many apples can you buy for P210?
- A. 12
- B. 14
- C. 15
- D. 16
- Answer: B (14).
- Hack (Ibig sabihin): Isang apple ay $60 / 4 = 15$ pesos. Kung may 210 pesos ka: $210 / 15 = 14$ .
A mixture of 20 liters of milk and water contains 10% water. How many liters of water must be added to make the water 20% of the new mixture?
- A. 2 liters
- B. 2.5 liters
- C. 3 liters
- D. 4 liters
- Answer: B (2.5 liters).
- Hack (Ibig sabihin): Ang tubig dati ay 2L. Milk ay 18L. Sa bagong mixture, ang 18L na milk ay magiging 80% (dahil 20% na ang water). $18 / 0.80 = 22.5$ (total mixture). Ang kailangang idagdag ay $22.5 - 20 = 2.5$ liters.
A man travels a distance of 18 km in 3 hours. He walks part of the way at 4 km/h and runs the rest at 10 km/h. How long did he run?
- A. 1 hour
- B. 1.5 hours
- C. 2 hours
- D. 0.5 hours
- Answer: A (1 hour).
- Hack (Ibig sabihin): Running = $x$ hrs, Walking = $3-x$ hrs. Distance: $10x + 4(3-x) = 18 \implies 6x + 12 = 18$ , so $6x = 6$ , $x = 1$ .
The ratio of the ages of two brothers is 3:5. If the older brother is 25 years old, how old is the younger brother?
- A. 10 years
- B. 12 years
- C. 15 years
- D. 18 years
- Answer: C (15 years).
- Hack (Ibig sabihin): $25$ years old ang mas matanda (ratio 5). So $25 / 5 = 5$ (isang part). Ang mas bata (ratio 3) ay $3 \times 5 = 15$ .
A store owner buys an item for P150 and sells it for P210. What is the percentage profit?
- A. 30%
- B. 35%
- C. 40%
- D. 50%
- Answer: C (40%).
- Hack (Ibig sabihin): Ang profit ay $210 - 150 = 60$ . Percentage profit: $(60 / 150) \times 100 = 40\%$ .

Tip: Drawing a small diagram or table can often help visualize complex word problems.