# Of the three numbers, the sum of the first two is 45; the sum of the second and

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1. Of the three numbers, the sum of the first two is 45; the sum of the second and third is 55 and...

Of the three numbers, the sum of the first two is 45; the sum of the second and third is 55 and
the sum of the third and thrice the first is 90. The third number is :

Options (1) 20                 (2) 25                    (3) 30                 (4) 3

2. My head says it is 30. The three numbers will be 20, 25 and 30 . 20+25=45, 25+30=55, 30+20*3=90. All is well that ends well.

3. (3) 30

Let a represent the first number, b the second, and c the third

Eq 1 a+b=45
Eq 2 b+c=55
Eq 3 3a+c=90

Solve Eq 1 for b: b=45-a
Substitute this into Eq 2: (45-a)+c=55
Simplify: c=10+a
Substitute into Eqn 3: 3a+(10+a)=90
Solve: a=20
Substitute a=20 into Eqn 3:
3(20)+c=90
Solve: c=30

4. The answers are:
A = 20
B = 25
C = 30

a+b = 20+25 = 45
b+c = 25 +30 = 55
c+3(a) = 30 + (3x20) = 30 +60 = 90

1. Well done.  Thanks for solving the problem

working