explain how to tdo this problem.
The larger of two numbers is 5 less than twice the smaller number. The sum of four times the larger and twice the smaller number is 100. If x is the smaller number what is the equations that determines the correct value of x
y = 2x-5
2x+4y = 100
Smaller no. = X.
Larger no. = 2x - 5.
4(2x - 5) + 2x = 100.
To solve this problem, we need to translate the given information into mathematical equations.
Let's call the larger number "L" and the smaller number "x" (as given in the question).
According to the problem:
1. "The larger of two numbers is 5 less than twice the smaller number" means L = 2x - 5.
2. "The sum of four times the larger and twice the smaller number is 100" means 4L + 2x = 100.
Now, we have two equations:
Equation 1: L = 2x - 5
Equation 2: 4L + 2x = 100
To determine the correct value of x, we need to solve this system of equations. We can do this using various methods, such as substitution, elimination, or graphing.
Let's use the substitution method here:
Substitute Equation 1 into Equation 2:
4(2x - 5) + 2x = 100
Simplify:
8x - 20 + 2x = 100
10x - 20 = 100
10x = 120
x = 12
Therefore, the correct value of x is 12.