Question

Find two consecutive whole numbers such that 4/7 of the larger exceeds 1/2 of the smaller by 5

Answer 1

The consecutive numbers are 62 and 63

Explanation:

Let the larger number be represented by x and the smaller number by y,

Provided they are consecutive numbers;

`x = y + 1` --- Equation 1

From the question; we have that

`(4x)/(7) = (y)/(2) + 5` --- Equation 2

Required

Find x and y

Multiply both sides of equation 2 by 14

`14 * (4x)/(7) = 14 * (y)/(2) + 14 * 5`

`2 * 4x = 7 * y + 70`

`8x = 7y + 70` ---- Equation 3

Substitute y + 1 for x in equation 2

`8(y + 1) = 7y + 70`

Open bracket

`8y + 8 = 7y + 70`

Collect like terms

`8y - 7y = 70 - 8`

`y = 62`

`x = y + 1`

So,

`x = 62 + 1`

`x = 63`

Hence, the consecutive numbers are 62 and 63