The difference of two numbers is 4. Three Times the smaller number is 4 more than twice the larger number. Find the numbers.
y-x = 4
3x = 2y+4
16 and 12
To solve this problem, we can set up a system of equations.
Let's assume the smaller number is x and the larger number is y.
From the given information, we can write the following equations:
1) The difference of two numbers is 4: y - x = 4
2) Three times the smaller number is 4 more than twice the larger number: 3x = 2y + 4
Now, we have a system of equations:
y - x = 4 ---> Equation (1)
3x = 2y + 4 ---> Equation (2)
To solve this system, we can use the substitution method or the elimination method.
Let's solve it using the substitution method:
From Equation (1), we can rewrite it as y = 4 + x.
Now, we substitute this expression for y in Equation (2):
3x = 2(4 + x) + 4
3x = 8 + 2x + 4
3x - 2x = 8 + 4
x = 12
Now, substitute the value of x back into Equation (1) to find y:
y - 12 = 4
y = 4 + 12
y = 16
So, the smaller number is 12 and the larger number is 16.