Question

The sum of three numbers is 15. If the second number is subtracted from the sum
of first and third numbers then we get 5. When the third number is subtracted from
the sum of twice the first number and the second number, we get 4. Find the three numbers.​

Answer 1

❍ Solution :-

Let the three numbers be x, y and z.

According to the given condition,

⇝ x + y + z = 15

∴ x + z - y = 5 that is x - y + z = 5

→ 2x + y - z = 4

$\sf D = |1, \: 1, \: \: 1 | \\ \: \: \: \: \: \: \: \: \: |1, - 1,1| \\ \: \: \: \: \: \: \: \: \: |2,1, - 1|$

= 1(1 - 1) -1(-1 - 2) +1(1 + 2)

= 1(0) - 1(-3) + 1(3)

= 0 + 3 + 3

= 6 ≠ 0

$\sf D_x = |15, \: 1, \: \: 1 | \\ \: \: \: \: \: \: \: \: \: \: \: |5, - 1, \: \: 1| \\ \: \: \: \: \: \: \: \: \: \: \: |4,1, - \: \: 1|$

= 15(1 - 1) -1(-5 - 4) + 1(5 + 4)

= 15(0) - 1(-9) + 1(9)

= 0 + 9 + 9

= 18

$\sf D_y = |1, \: 15, \: - 1 | \\ \: \: \: \: \: \: \: \: \: \: \: |1, \: \: \: 5, \: \: \: \: \: 1| \\ \: \: \: \: \: \: \: \: \: \: \: |2, \: \: 4, \: \: - 1|$

= 1(-5 - 4) -15(-1 - 2) +1(4 - 10)

= 1(-9) - 15(-3) + 1(-6)

= -9 + 45 - 6

= 30

$\sf D_z = |1, \: 1, \: 15 | \\ \: \: \: \: \: \: \: \: \: \: \: |1, \: - 1, 5| \\ \: \: \: \: \: \: \: \: \: \: \: |2, \: \: 1, \: \: 4|$

= 1(-4 - 5) -1(-4 - 10) +15(1 + 2)

= 1(-9) -1(-14) + 15(3)

= -9 +14 + 45

= 42

By Cramer's Rule,

$\sf →x = \dfrac{D_x}{D} = \dfrac{18}{6} = 3$

$\sf →y = \dfrac{D_y}{D} = \dfrac{30}{6} = 5$

$\sf →z = \dfrac{D_z}{D} = \dfrac{42}{6} = 7$

Hence the three numbers are 3, 5 and 7.

Answer 2

Answer:

$\huge{\underbrace{\boxed{\tt{3 , 5 , 7}}}}$

Step-by-step explanation:

Let say three numbers are

Let say three numbers area , b , c

$\sf{a + b + c = 15}$ equation 1

$\sf{a + c - b = 5}$ equation 2

$\sf{2a + b - c = 4}$ equation 3

$\sf{Equation 1 - Equation 2}$

$\sf :\longmapsto{ 2b = 10}$

$\sf :\longmapsto{b = 5}$

$\sf{Equation \:2 + equation \:3}$

$\sf{3a = 9}$

$\sf :\longmapsto{a = 3}$

Putting un equation 1 a & b values

$\sf{3 + 5 + c = 15}$

$\sf :\longmapsto{c = 7}$

• Hence, the three numbers are 3, 5 and 7 respectively