Question

The sum of two numbers is 184
If one third of the one exceeds
one seventh of the other by 8,
ind the smallest number..​

Answer 1

Answer:

Smaller number = 72

Step-by-step explanation:

Let the first number be x

Let the second number be y

We are given that the sum of two numbers is 184

So,

$x + y = 184....(1)$

Now we are given that one-third of the one exceeds one - seventh of the other by 8

So, A.T.Q

$\frac{x}{y} - \frac{y}{7} = 8 \\ \frac{7x - 3y}{21} = 8 \\ 7x - 3y = 8 \times 21 \\ 7x - 3y = 168....(2)$

Now substitute the value of x from 1 in 2

$7(184 - y) - 3y = 168 \\ 1288 - 7y - 3y = 168 \\ 1288 - 168 = 10y \\ 1120 = 10y$

So, y =112

Substitute the value of y in 1

$x + 112 = 184 \\ x = 184 - 112 \\ x = 72$

Hence the smaller number is 72.....

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