The difference between the first and second number is zero. Find the numbers such that the difference between thrice the first and twice the second is 18.
If the two numbers are a and b
a-b=0
3a-2b = 18
since a=b,
3a-2a=18
a = 18
So, b=18
To find the numbers, we can start by assigning variables. Let's call the first number "x" and the second number "y."
According to the problem, the difference between the first and second number is zero. Mathematically, this can be represented as:
x - y = 0 (Equation 1)
The problem also states that the difference between thrice the first number and twice the second number is 18. Mathematically, this can be represented as:
3x - 2y = 18 (Equation 2)
Now, we have a system of two equations with two unknowns. We can solve this system using any appropriate method, such as substitution or elimination.
Let's solve it using the substitution method:
1. Solve Equation 1 for x in terms of y:
x = y (since x - y = 0, we can add y to both sides)
2. Substitute this value of x into Equation 2:
3(y) - 2y = 18
Simplifying this equation, we get:
3y - 2y = 18
y = 18
3. Substitute the value of y into Equation 1 to find x:
x = y
x = 18
Therefore, the first number (x) is 18 and the second number (y) is also 18.