the difference of two numbers is 4 .3 times the smaller number is 4 more than twice the larger number. find the numbers
let the smaller be x
then the larger is x+4
3x = 2(x+4) + 4
Solve and state your conclusion.
3x=2(x+4)+4
3x=2x+8+4
3x=2x+12
12=
3x=2(x+4)+4
3x=2x+8+4
3x=2x+12
12=3x-2x
12=1x
x=12
To solve this problem, we can set up a system of equations using the information given.
Let's assume the smaller number is "x" and the larger number is "y."
According to the problem, the difference between the two numbers is 4, so we have the equation:
Equation 1: y - x = 4
The problem also states that 3 times the smaller number is 4 more than twice the larger number, which can be expressed as:
Equation 2: 3x = 2y + 4
Now, we can solve the system of equations:
Step 1: Rearrange Equation 1 to solve for y:
y = x + 4
Step 2: Substitute this value of y into Equation 2:
3x = 2(x + 4) + 4
3x = 2x + 8 + 4
3x = 2x + 12
3x - 2x = 12
x = 12
Step 3: Substitute the found value of x back into Equation 1 to solve for y:
y - 12 = 4
y = 16
Therefore, the smaller number is 12 and the larger number is 16.