The document provides various examples of word problems involving equations in one variable, categorized into age, digit, geometry, distance, money, and mixture problems. Each category includes multiple examples with representations, equations, and solutions related to the problem at hand. The focus is on using algebraic methods to solve real-life scenarios involving relationships between different quantities.

1. WORD PROBLEMS
INVOLVING EQUATIONS IN
ONE VARIABLE
(AGE PROBLEMS)

2. Example #1: Vio is now 24 years older than his brother.
Find their present ages if he will be twice as old as his
brother in 6 years.
Representation
:
x = present age of Vio’s
brother
Present Future
Vio
brother
x + 24
x
(x + 24) + 6
x + 6
Equation: (x + 24) + 6 = 2 (x + 6)

3. Example #2: The sum of the ages of Kerby and his
cousin is 42. How old is Kerby if he is 8 years younger
than his cousin?
Representation
:
x = present age of Kerby’s cousin
Present
Kerby
cousin
x - 8
x
Equation: x + (x – 8) = 42

4. Example #3: Six years ago, Eizen was 12 year younger
than twice his sister’s age. How old is Eizen if he is
thrice as old as his sister now.
Representation
:
x = present age of Eizen’s
sister
Present Past
Eizen
sister
2x
x
2x - 6
x - 6
Equation: 2x – 6 = 3 (x – 6) - 12

5. WORD PROBLEMS
INVOLVING EQUATIONS IN
ONE VARIABLE
(DIGIT PROBLEMS)

6. Example #1: Find the two-digit number if the sum of
its digits is 8. The number is 11 times its units digit.
Representation
:
x = units digit
Equation: 10 (8 – x) + x = 11x
8 - x = tens digit

7. Example #2: The number is more than three times the
sum of the digits. Find the two-digit number if the tens
digit is less than the units digit.
Representation
:
x = units digit
Equation: 10 (x - 3) + x = 3 [(x – 3) + x] + 4
x - 3 = tens digit

8. Example #3: Find the original two-digit number. Its
tens digit is thrice the units digit. When digits are
reversed, the new number is 147 less than two times
the original number.
Representation
:
x = units digit
Equation: 10x + 3x = 2 [10 (3x) + x] -147
3x = tens digit

9. WORD PROBLEMS
INVOLVING EQUATIONS IN
ONE VARIABLE
(GEOMETRY PROBLEMS)

10. Example #1: The perimeter of a rectangle is 84 cm. Its
length is 12 cm longer than its width. Find the length?
Representation
:
x = width
Equation: P = 2L + 2W
x + 12 = length
P = 84 cm
84 = 2 (x + 12) +2x

11. Example #2: The perimeter of a rectangle is 72 cm. Its
width is 11 cm longer than its length. Find the width?
Representation
:
x = length
Equation: P = 2L + 2W
x + 11 = width
P = 72 cm
72 = 2 (x + 11) +2x

12. Example #3: One angle measures 30º less than two
times its supplement. Find the measure its
supplement.
Representation
:
x = supplement
Equation: x + 2x – 30º = 180º
2x - 30º = measure of the angle

13. Example #4: One angle measures 20º more than its
complement. Find the measure of the complement.
Representation
:
x = complement
Equation: x + (x + 20º) = 90º
x + 20º = measure of the angle

14. WORD PROBLEMS
INVOLVING EQUATIONS IN
ONE VARIABLE
(DISTANCE PROBLEMS)

15. Example #1: Two planes are 3 600 miles apart and fly
toward each other. Their rates differ by 90 miles per
hour. Find the rates if they will meet after 5 hours.
Representation
:
Rate
Plane A
5x + 5 (x + 90) = 3 600
Time Distance
Plane B
x 5 5x
x + 90 5 5 (x + 90)
Equation: D1 + D2 = DT

16. Example #2: Kerby spends 3 hours training. He runs at 8
miles per hour then he walks back to the starting point at 2
miles per hour. How long does he spend walking? How long
does he spend running?
Representation
:
Rate
Running
8x = 2 (3 – x)
Time Distance
Walking
8 x 8x
2 3 - x 2 (3 - x)
Equation: D1 = D2

17. Example #3: Bus A and Bus B started from one point and
travelled to opposite directions. Bus A travelled at 60 kph and
Bus B at 70 kph, how long will they be 650 km apart?
Representation
:
Rate
Bus A
60x + 70x = 650
Time Distance
Bus B
60 x 60x
70 x 70x
Equation: D1 + D2 = DT

18. WORD PROBLEMS
INVOLVING EQUATIONS IN
ONE VARIABLE
(MONEY PROBLEMS)

19. Example #1: A coin can has 5 peso and 1 peso coins. If
there are 12 more 5 peso coins than 1 peso coins, how
many of each kind are there in the coin can if the total
amount is 600 pesos?
Representation
:
x = 1 peso coins
Equation: x + 5 (x + 12) = 600
x + 12 = 5 peso coins

20. Example #2: Mr. Vite has 5 500 pesos in 100 peso bills
and 50 peso bills in his money box. He has 80 bills in
the money box. How many bills of each kind does he
have?
Representation
:
x = 50 peso bills
Equation: 50x + 100 (80 – x) = 5 500
80 - x = 100 peso bills

21. Example #3: Teacher Melvs got his salary in 1 000 peso
bills and 500 peso bills. The number of 1 000 peso bills
he got was 5 more than one-half the number of 500
peso bills. His salary is 25 000 pesos. How many bills
of each kind did he get?
Representation
:
x = 500 peso bills
Equation: 500x + 1 000 (
1
2
x + 5) = 25 000
1
2
x + 5 = 1 000 peso bills

22. WORD PROBLEMS
INVOLVING EQUATIONS IN
ONE VARIABLE
(SOLUTION/MIXTURE
PROBLEMS)

23. Example #1: How many gallons of solution with 30%
alcohol to be mixed with solutions with 40% alcohol to
obtain 50 gallons of solution with 35% alcohol?
Representation
: Number of
Gallons
Solution 1
Equation: .30x + .40 (50 – x) = .35 (50)
Percent of
Alcohol
Amount of
Alcohol
Solution 2
Solution 3
x
50 - x
50
30% = .30
40% = .40
35% = .35
.30x
.40 (50 – x)
.35 (50)

24. Example #2: How many kg of pili nuts at 75 pesos per
kg should I add to 30 kg of cashew nuts at 100 pesos
per kg if the mixture would costs 90 pesos per kg?
Representation
: Cost per
Kilogram
Pili Nuts
Equation: 75x + 100 (30) = 90 (25 + x)
Kilogram
Cashew
Nuts
Mixture
75
100
90
x
30
25 + x