Question

One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Find the two numbers.​

Answer 1

One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Then the two numbers are 5 and 7

Solution:

Given that one number is 7 less than a second number.

Twice the second number is 1 less than 5 times the first.

Need to determine two numbers.

Let assume first number be represented by variable x and second number be represented by variable y.

As first number is 7 less than a second number, adding 7 to first number will give us second number

=> x + 7 = y ------ (1)

`\begin{array}{l}{\text { Twice of second number }=2 * \text { second number }=2 * y=2 y} \\\\ {\text { 5 times the first number }=5 * \text { first number }=5 * x=5 x}\end{array}`

As given that Twice the second number is 1 less than 5 times the first , if we 1 to twice of second number we will get 5 times first number ,

=> 2y + 1 = 5x ------ (2)

On substituting value of y as x + 7 from equation 1 into equation 2 , we get

2(x + 7) + 1 = 5x

=> 2x + 14 + 1 = 5x

=> 2x – 5x = -15

=> -3x = -15

x = 5

Substituting x = 5 in equation (1) to get value of y

=> y = 5 + 7 = 12

Hence first number is 5 and second number is 12