Question

5. Two numbers are such that if 7 is added to the first
number, a number twice the second number is
obtained. If 20 is added to the second number,
the number obtained is four times the first number
Find the two numbers.​

Answer 1

Answer:

$\bigstar{\bold{First\:number=\dfrac{47}{7}}}$

$\bigstar{\bold{Second\:number=\dfrac{48}{7} }}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• If 7 is added to the first number, a umber twice the second number is obtained.
• If 20 is added to the second number, the number obtained is four times the first number

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The two numbers

$\Large{\underline{\underline{\bf{Solution:}}}}$

➡ Here let as assume the first number as x

➡ Let the second number be y

➡ By first case,

    x + 7 = 2 y

    x = 2y - 7-----(1)

➡ By the second case,

    y + 20 = 4x---(2)

➡ Substitute the value of x from equation 1 in equation 2

    y + 20 =  4 × (2y - 7)

    y + 20 = 8y - 28

    y - 8y = -28 - 20

   -7y = -48

      y = 48/7

➡ Hence the second number is 48/7

    $\boxed{\bold{Second\:number=\dfrac{48}{7} }}$

➡ Substitute the value of y in equation 1

    x = 2 × 48/7 - 7

    x = 96/7 - 7

    x = 96/7 - 49/7

    x = 47/7

➡ Hence the first number is 47/7

    $\boxed{\bold{First\:number=\dfrac{47}{7}}}$

$\Large{\underline{\underline{\bf{Verifcation:}}}}$

➡ x + 7 = 2y

   47/7 + 7 = 2 × 48/7

   47/7 + 49/7 = 96/7

   96/7 = 96/7

➡ y + 20 = 4 x

    48/7 + 20 = 4 × 47/7

    48/7 + 140/7 = 188/7

    188/7 = 188/7

➡ Hence verified.