Question

there are two consecutive numbers such that one fifth of the greater exceeds one seventh of the lesser by 3 find the number.
(EXPLAIN WITH STEPS)

Answer 1

Hi there ! good question,

well , here the method,

let one number be x

Since the numbers are consecutive,

other number = x + 1

Given,
one fifth of the greater exceeds one seventh of the lesser by 3 find the number.

So, we will break the words into number step by step,

1/5th of the greater number which is x + 1

so,

$\frac{1}{5} (x + 1) = \frac{x + 1}{5}$

1/7th of the lesser number = x

$= \frac{1}{7} x = \frac{x}{7}$

Also,
it greater number exceeds the smaller number by 3.

in simple language , this means that the greater number is 3 greater than the smaller number.

Since , it's an equation, LHS = RHS

so,

$\frac{x + 1}{5} = \frac{x}{7} + 3$
transposing x/7 to LHS,
we have,

$\frac{x + 1}{5} - \frac{x}{7} = 3$
LCM = 35

$\frac{7(x + 1) - 5x}{35} = 3$

$\frac{7x + 7 - 5x}{35} = 3$

$\frac{2x + 7}{35} = 3$

$2x + 7 = 3 \times 35$

$2x + 7 = 105$

$2x = 105 - 7$

$2x = 98$

$x = \frac{98}{2}$
$x = 49$

So,

one number = x = 49

second number = 49 + 1 = 50

Answer 2

Let the two consecutive numbers be x + 1 and x + 2.

Given that 1/5th of the greater exceeds 1/7th of the lesser by 3.

1/5(x + 2) = 1/7(x + 1) + 3

1/5x + 2/5 = 1/7x + 1/7 + 3

1/5x + 2/5 = 22 + x/7

1/5x = x + 22/7 - 2/5

7x = 5(x + 22) - 14

7x = 5x + 110 - 84

7x = 5x + 96

2x = 96

x = 48.


Therefore the 1st number = 48 + 1

                                            = 49.


Therefore the 2nd number = 48 + 2

                                              = 50.


Therefore the numbers are 49 and 50.


Hope this helps!