Question

The sum of two positive integers is 115. The integers are in the ratio 2:3. Find the integers​

Answer 1

Given :

• Sum of two positive integers = 115
• Ratio of those integers = 2 : 3

To Find :

• The integers

Solution :

Let the ratio constant be "x"

Then the numbers are 2x and 3x .

We are given that sum of those two integers (2x and 3x) as 115.

$\\ : \implies \sf \: 2x + 3x = 115$

$\\ : \implies \sf \: 5x = 115$

$\\ : \implies \sf \: x = \frac{115}{5}$

$\\ : \implies {\underline{\boxed{\pink{\mathfrak{\:x = 23}}}}} \: \bigstar$

Now , The numbers are ;

• 2x = 2(23) = 46
• 3x = 3(23) = 69

$\\ \therefore{\underline{\sf{Hence \: , \: The \: Required \: Integers \: are \: \bold{ 46} \: and \: \bold{69}}}}$

Answer 2

✪ Assumption ✪ :-

• Let us assume the numbers to be x and y
• It is given that they are in ratio 2:3

✪ Process ✪:-

Since they are in the ratio 2:3 , then x:y will be 2:3

$\frac{x}{y}=\frac{2}{3}$

$y=\frac{3x}{2}$ $=1.5x$

Now, it is given that their sum is 115.

So, x + y = 115

Substituting y in terms of x, we get :

x + 1.5x = 115

2.5x = 115

$\boxed{x=46}$

So, for finding y, substitute x. We get:

y = 1.5x =(1.5)(46)

$\boxed{y=69}$

So , the numbers are 46 and 69.