The difference between two numbers is 18. If the sum of three times the smaller number and half the larger number is 2, find the smaller number.
if x is smaller and y is larger
y - x = 18
3x + y/2 = 2
(x,y) = (-2,16)
To find the smaller number, we need to set up a system of equations based on the given information.
Let's assume the smaller number is x, and the larger number is y.
From the first statement, "the difference between two numbers is 18," we can write the equation:
y - x = 18
From the second statement, "the sum of three times the smaller number and half the larger number is 2," we can write the equation:
3x + 0.5y = 2
Now we can solve this system of equations to find the values of x and y.
Let's use the substitution method to solve the system:
1. Rearrange the first equation to solve for y:
y = x + 18
2. Substitute this expression for y in the second equation:
3x + 0.5(x + 18) = 2
3x + 0.5x + 9 = 2
3. Combine like terms:
3.5x + 9 = 2
4. Move the constant term to the other side:
3.5x = 2 - 9
3.5x = -7
5. Divide both sides by 3.5 to solve for x:
x = -7 / 3.5
x = -2
Therefore, the smaller number x is -2.