One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.
Let x be the larger number.
Solve this equation:
x -12 + 2x = 39
If you are unfamiliar with algebra, try different integers between 15 and 20, for the larger number, and see which one "works"
To solve this problem, we can set up a system of equations.
Let's assume that the smaller number is represented by x, and the larger number is represented by y.
According to the problem, one number is 12 more than another. So we have the equation:
y = x + 12 ---(1)
The sum of the smaller number and twice the larger number is 39. So we have the equation:
x + 2y = 39 ---(2)
Now we can solve this system of equations.
Substitute the value of y from equation (1) into equation (2):
x + 2(x + 12) = 39
Simplify the equation:
x + 2x + 24 = 39
Combine the x terms:
3x + 24 = 39
Subtract 24 from both sides:
3x = 39 - 24
Simplify the equation:
3x = 15
Divide both sides by 3:
x = 5
Now substitute the value of x into equation (1) to find the value of y:
y = x + 12
y = 5 + 12
y = 17
Therefore, the larger number is 17.