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## Explanation

- Of the three numbers the sum of the first two is 45.
- The sum of the second and third is 55.
- The sum of the third and thrice the first is 90.
- The third number can be figure out in this way.

Let suppose three number are a, b and c.

The sum of a and b (first two) is 45.

a + b = 45 ________ (i)

The sum of b and c (second and third) is 55.

b + c = 55 ________ (ii)

The sum of c and 3a (third and thrice the first) is 90.

c + 3a = 90 ________ (iii)

By solving these three equations simultaneously, we can easily figure out the third number (c = 30).

## To Find

Third Number = ?

## Solution

Let suppose three number are a, b and c.

According to the given conditions

a + b = 45 ________ (i)

b + c = 55 ________ (ii)

c + 3a = 90 ________ (iii)

Subtracting equation (ii) from (i)

a + b – b – c = 45 – 55

a – c = -10 ________ (A)

Adding equation (A) and (iii)

a – c + c + 3a = -10 + 90

a + 3a = 80

4a = 80

a = 80/4

a = 20

Put a = 20 in equation (iii)

c + 3(20) = 90

c + 60 = 90

c = 90 – 60

c = 30

**Third Number = 30 answer**

## Conclusion

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 first is 90. The third number is 30.