Question

A number is 4 times another number if 21 is added to both then first number becomes 7/4 times the other. What are the number?

Answer 1

To Find:-

• Find the numbers.

Given:-

• A number is 4 times another number if 21 is added to both then first number becomes 7/4 times the other.

Solution:-

Let the two numbers be x and y.

A number is 4 times another number,

➣ x = 4y ….. (1)

➣ (x + 21)/(y + 21) = 7/4

➣ 4(x + 21) = 7(y + 21)

➣ 4x + 84 = 7y + 147

➣ 4x - 7y = 147 - 84

➣ 4x - 7y = 63  ...... ( 2 )

Substitute x in equation 2.

➣ 4(4y) - 7y = 63

➣ 16y - 7y = 63

➣ 9y = 63

➣ y = 63/9

➣ $\boxed{\bf{\color{yelow}{ \: y \: = \: 7 \: }}}$

Now,

Substitute y in equation 1.

➣ x = 4(7)

➣ $\boxed{\bf{\color{yelow}{ \: x \: = \: 28 \: }}}$

Verification:-

➣ x = 4y

➣ 28 = 4(7)

➣ $\boxed{\bf{\color{yelow}{ \: 28 \: = \: 28 \: }}}$

Answer 2

To Find:-

Find the numbers.

Given:-

A number is 4 times another number if 21 is added to both then first number becomes 7/4 times the other.

Solution:-

Let the two numbers be x and y.

A number is 4 times another number,

➣ x = 4y ….. (1)

➣ (x + 21)/(y + 21) = 7/4

➣ 4(x + 21) = 7(y + 21)

➣ 4x + 84 = 7y + 147

➣ 4x - 7y = 147 - 84

➣ 4x - 7y = 63 ...... ( 2 )

Substitute x in equation 2.

➣ 4(4y) - 7y = 63

➣ 16y - 7y = 63

➣ 9y = 63

➣ y = 63/9

$y \: = 7$

Now,

Now,Substitute y in equation 1.

➣ x = 4(7)

$x \: = 28$

Verification:-

➣ x = 4y

➣ 28 = 4(7)

$28 = 28$