Question

8. The sum of four numbers is 119. When 3 and 7 are
added to the first two; 5 and 8 are subtracted from
the 3rd and 4th, the numbers will be equal. Find the
sum of the largest number and the smallest
number.​

Answer 1

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Answer 2

Given:

The sum of four numbers is 119

When 3 and 7 are  added to the first two; 5 and 8 are subtracted from  the 3rd and 4th, the numbers will be equal

To Find:

The sum of the largest number and the smallest  number

Solution:

Let the four numbers be a, b, c, and d such that a < b < c < d.

According to the question,

a + b + c + d = 119      - (1)

Also,

(a+7) = (b+3) = (c-5) = (d-8)     - (2)

⇒ b = a + 7 - 3

= a + 4                      - (3)

⇒ c = d - 8 + 5

= d - 3                   - (4)

Substituting from equantions (4) and (3) in (1)

a + (a+4) + (d-3) + d = 119

or 2a + 4 + 2d - 3 = 119

or 2a + 2d = 119 - 1

or a + d = 118 / 2

or a + d = 59

Hence, the  sum of the largest number and the smallest  number is 59.