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

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(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

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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

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Well done. Thanks for solving the problem

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.

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