Question

6= The sum of three numbers is 57. If twice the first number is 6 less than the second and the second number is
10 more than the third, find the numbers.
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Answer 1

Step-by-step explanation:

Consider the numbers x, y, z.

Condition 1:- x + y + z = 57..........(1)

Condition 2:- 2x = y - 6...........(2)

Condition 3:- y = 10 + z ...........(3)

2x = y - 6 [Equation (2)]

2x + 6 = y

i.e. y = 2x + 6 .............(4)

y = 10 + z [Equation (3)]

y - 10 = z

i.e. z = y - 10

= 2x + 6 - 10 [From (4)]

z = 2x - 4 ...........(5)

x + y + z = 57 [Equation (1)]

x + 2x + 6 + 2x - 4 = 57 [From (4) & (5)]

5x + 2 = 57

5x = 57 - 2

5x = 55

x = 55

5

x = 11 ..........(6)

y = 2x + 6 [Equation (4)]

y = 2(11) + 6 ...........[From (6)]

y = 22 + 6

y = 28

z = 2x - 4 [Equation (5)]

z = 2(11) - 4 ..........[From (6)]

z = 22 - 4

z = 18

Therefore, x = 11

y = 28

z = 18