Question

1. If from twice the greater of two numbers, 20 is subtracted, the result isthe other number. If from twice the smaller number, 5 is subtracted, the result is the greater number. Find the numbers

Answer 1

Given:

(i)  If from twice the greater of two numbers, 20 is subtracted, the result isthe other number.

(ii) If from twice the smaller number, 5 is subtracted, the result is the greater number.

To find:

(i) The two numbers

Solution:

Let the bigger number be 'x' and the smaller number be 'y'.

For the first case, twice the bigger number subtracted by  20,gives the smaller number. So,

y = 2x - 20   ...(1)

For the second case, twice the second number subtracted by 5, gives the smaller number.

So,

x = 2y - 5

Replacing the value of 'y' from (1), we get,

x = 2(2x-20) - 5

= 4x - 40 - 5

= 4x - 45

⇒ 3x = 45

⇒ x = 45/3

⇒ x = 15

y = 2(15)- 20

= 30 - 20

= 10

So, the numbers are 15 and 10.

Answer 2

Answer:

Given:

(i)  If from twice the greater of two numbers, 20 is subtracted, the result isthe other number.

(ii) If from twice the smaller number, 5 is subtracted, the result is the greater number.

To find:

(i) The two numbers

Solution:

Let the bigger number be 'x' and the smaller number be 'y'.

For the first case, twice the bigger number subtracted by  20,gives the smaller number. So,

y = 2x - 20   ...(1)

For the second case, twice the second number subtracted by 5, gives the smaller number.

So,

x = 2y - 5

Replacing the value of 'y' from (1), we get,

x = 2(2x-20) - 5

= 4x - 40 - 5

= 4x - 45

⇒ 3x = 45

⇒ x = 45/3

⇒ x = 15

y = 2(15)- 20

= 30 - 20

= 10

So, the numbers are 15 and 10.

Step-by-step explanation: