Answer:
The two numbers are 17 and 7
Explanation:
Translate this word problem into a math equation
If we let x and y be the two unknown numbers
One-half the sum of two numbers is 12 ==>
- sum of two numbers : x + y
- one-half the sum of two numbers : (1/2)(x + y)
- one-half the sum of two numbers is 12: (1/2)(x + y) =12
So one equation is 1/2(x + y) =12
Multiplying throughout by 2 gets rid of the denominator:
2 x 1/2 x (x + y) = 2 x 12
x + y = 24 (1)
One of the numbers is three more than two times the other number:
x = 2y + 3
or
x - 2y = 3 (2)
Equation (2) - Equation (1) =>
x + y - (x -2y) = 24 - 1
x + y - x + 2y = 21
3y = 21
y = 21/3
y = 7
With y = 7, substituting in equation 1 gives
x + y = 24
x + 7 = 24
x = 24-7
x = 17
The two numbers are 17 and 7