Respuesta :
The larger number is 13 and smaller number is 4
Solution:
Let the larger number be "a"
Let the smaller number be "b"
Given that larger of two numbers is twice the smaller increased by five
larger number = twice the smaller increased by five
larger number = twice the smaller number + 5
a = 2b + 5 --- eqn 1
Also given that three times the larger exceeds double the smaller by 31
Here "exceeds" denotes addition and "times" denotes multiplication
"double" denotes being multiplied by 2
three times the larger number = double the smaller number + 31
3a = 2b + 31 ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "b"
Substitute eqn 1 in eqn 2
3(2b + 5) = 2b + 31
6b + 15 = 2b + 31
6b - 2b = 31 - 15
4b = 16
b = 4
From eqn 1,
a = 2b + 5
a = 2(4) + 5
a = 8 + 5
a = 13
Thus the larger number is 13 and smaller number is 4
