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NUMBER PROBLEMS
PROBLEM 1:
 The
sum of 2 counting numbers is 8. If
twice the smaller is two less than the
larger number, find the two numbers.
STUDY THE TABLE.
1st number
2nd number
Case 1:
1
Case 2:
2
8-
Case 3:
3
8- 3 = 5
Case 4:
4
8- 4 = 4
Case 5
5
8–5= 3
Case 6:
6
8-6= 2
Case 7:
7
8-7= 1
8
1= 7
2= 6
If x is the 1st and the smallest
number, then, 8-x is the other or
the larger number.
REPRESENTATION:
Let x=1st number (smaller)
8-x=2nd number (larger)
Equation:
(Twice the smaller is two less than the larger.)
2(smaller) is two less than the larger number.
2
x
=
8-x
-
2
2X=8-X-2
Solution:
x+ 2x = 6 -x +x
(1/3) 3x = 6 (1/3)
x =2
2nd number = 8-x
= 8-2
= 6
1st number
Therefore, the two numbers
are 2 and 6.
PROBLEM 2:
The sum of three numbers is 134. The second
number is 5 more than the first, and the third is
4 more than three times the second. Find the
numbers.
ARROW DIAGRAM
The second number is 5 more than the first.
2nd
1st
3rd
The third number is 4 more than thrice the second.
2nd
1st
3rd
Putting the two illustration together,
2nd
1st
3rd
It shows that it is the 1st number which is in the last
arrow head,
Therefore the first number=x
The second number is 5 more than the first.
2nd number
= x
+
5
The 3rd no. is 4 more than three times the second.
3rd number
=
3(x + 5)
+
4
Representation:
Let x = 1st no.
x+5 = 2nd no.
3(x+5)+4= 3rd no.
Equation:
(The sum of three numbers is 134.)
1st + 2nd + 3rd
is 134
x + x+5 +3(x+5)+4 = 134
Solution:
x+x+5+3(x+5)+4=134
x+x+5+3x+15+4=134
5x+24=134
5x=134-24
5x=110
x=22
x+5=22+5=27
3(x+5)+4=3(22+5)+4=85
The three numbers are 22,
27, and 85
EXERCISES:
1. The sum of two numbers is 60. The larger
number is three times the smaller number. Find
the numbers.
2. When 5 times a number is increased by 45, the
answer is the same as when 105 is decreased by
that number. Find the number.
God is Good All the Time. 
Prepared by: Cherryl M. Cortez
III-B BSE MATH