Answer:
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;
[tex]x=2y+5[/tex] ⇒equation 1
Also Given:
Three times the larger exceeds double the smaller by 31
[tex]3x=2y+31[/tex] ⇒equation 2
Now Substituting the value of x from equation 1 in equation 2 we get;
[tex]3(2y+5) = 2y+31[/tex]
Now Using Distributive property we get;
[tex]6y+15 = 2y +31[/tex]
Combining the like terms we get;
[tex]6y-2y = 31-15[/tex]
Now Using Subtraction property we get;
[tex]4y =16[/tex]
Now Using Division property we get;
[tex]\frac{4y}{4}=\frac{16}{4}\\\\y =4[/tex]
Now Substituting value of y in equation 1 we will find the value of x.
[tex]x=2y+5\\\\x = 2\times4+5\\\\x=8+5\\\\x=13[/tex]
Hence Larger number is 13 and Smaller number is 4.
