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Sagot :
A. Number Problem: Consecutive Numbers
First number: x
Second Number: x + 1
Third Number: x + 2
Sum the three consecutive numbers: 27
Equation:
(x) + (x+1) + (x+2) = 27
3x + 3 = 27
3x = 27 - 3
3x = 24
3x/3 = 24/3
x = 8
The three consecutive numbers: substitute 8 for x.
First number: x = 8
Second number: x+1 ⇒ 8+1 = 9
Third number: x+2 ⇒ 8+2 = 10
The three consecutive numbers are 8, 9, and 10
Check:
8 + 9 + 10 = 27
17 + 10 = 27
27 = 27
(Note; For consecutive even or odd integers/numbers, represent with x as the first number, x+2 as second, x+4, as third, x+6 as fourth,...)
B. Age Problem/Comparison problem:
Fred is person of reference or the person James is compared.
Representation of the present ages:
Fred: x
James: 2x (twice as old as the person of reference, Fred)
After 5 years (add 5 to each age):
Fred: x + 5
James: 2x + 5
Sum of the ages in five years: 43
Equation:
(x+5) + (2x+5) = 43
x + 2x + 5 + 5 = 43
3x + 10 = 43
3x = 43 - 10
3x = 33
3x/3 = 33/3
x = 11
Present ages:
Fred: x = 11
James: 2x ⇒ 2(11) = 22
Final Answer: At present, Fred is 11 years old and James is 22 years old.
In 3 years, Fred is 14 years old:
11 + 3 = 14
14 = 14
In five years, the sum of their ages is 43.
Fred: 11 + 5 = 16
James: 22 + 5 = 27
16 + 27 = 43
43 = 43
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TIP:
The word "is" means equal (=).
Twice means two times
Thrice means three times.
Example:
A is four more than three times the age of B. B is twice the age of C. C's age is the point of reference, so his age represents x.
C = x
B = 2x
A = 4 + 3 (2x) or 4 + 6x
First number: x
Second Number: x + 1
Third Number: x + 2
Sum the three consecutive numbers: 27
Equation:
(x) + (x+1) + (x+2) = 27
3x + 3 = 27
3x = 27 - 3
3x = 24
3x/3 = 24/3
x = 8
The three consecutive numbers: substitute 8 for x.
First number: x = 8
Second number: x+1 ⇒ 8+1 = 9
Third number: x+2 ⇒ 8+2 = 10
The three consecutive numbers are 8, 9, and 10
Check:
8 + 9 + 10 = 27
17 + 10 = 27
27 = 27
(Note; For consecutive even or odd integers/numbers, represent with x as the first number, x+2 as second, x+4, as third, x+6 as fourth,...)
B. Age Problem/Comparison problem:
Fred is person of reference or the person James is compared.
Representation of the present ages:
Fred: x
James: 2x (twice as old as the person of reference, Fred)
After 5 years (add 5 to each age):
Fred: x + 5
James: 2x + 5
Sum of the ages in five years: 43
Equation:
(x+5) + (2x+5) = 43
x + 2x + 5 + 5 = 43
3x + 10 = 43
3x = 43 - 10
3x = 33
3x/3 = 33/3
x = 11
Present ages:
Fred: x = 11
James: 2x ⇒ 2(11) = 22
Final Answer: At present, Fred is 11 years old and James is 22 years old.
In 3 years, Fred is 14 years old:
11 + 3 = 14
14 = 14
In five years, the sum of their ages is 43.
Fred: 11 + 5 = 16
James: 22 + 5 = 27
16 + 27 = 43
43 = 43
--------------------------------------------------
TIP:
The word "is" means equal (=).
Twice means two times
Thrice means three times.
Example:
A is four more than three times the age of B. B is twice the age of C. C's age is the point of reference, so his age represents x.
C = x
B = 2x
A = 4 + 3 (2x) or 4 + 6x
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