The larger of two numbers is twice the smaller increased by five. find the two numbers if three times the larger exceeds double the smaller by 31

Larger number is 13 and Smaller number is 4.

Step-by-step explanation:

Let the larger number be x.

Also let the smaller number be y.

We need to find the two numbers.

Given:

The larger of two numbers is twice the smaller increased by five.

framing in equation form we get;

⇒equation 1

Also Given:

Three times the larger exceeds double the smaller by 31

⇒equation 2

Now Substituting the value of x from equation 1 in equation 2 we get;

Now Using Distributive property we get;

Combining the like terms we get;

Now Using Subtraction property we get;

Now Using Division property we get;

Now Substituting value of y in equation 1 we will find the value of x.

Hence Larger number is 13 and Smaller number is 4.