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I don't know how Age and Number Problems work! I have an exam tomorrow D:. Help please.


Here's an ex:
the sum of three consecutive numbers is 27. What are the numbers? (NUMBER PROBLEM)

James is twice as old as Fred. Three years from now, Fred will be 14 years old. What are their current ages if, after 5 years, the sum of their ages is 43? (AGE PROBLEM)

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
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