Four times the sum of a number and four is the same as two multiplied by two less than three times the number. What is the solution to this problem?
Let's assume the number is x.
The sum of a number and four is x + 4.
Four times the sum of a number and four is 4(x + 4) = 4x + 16.
Two less than three times the number is 3x - 2.
According to the problem, 4x + 16 = 2(3x - 2).
Simplifying the equation, we get 4x + 16 = 6x - 4.
Bringing the variables to one side, we have 6x - 4x = 16 + 4.
Simplifying, we get 2x = 20.
Dividing both sides by 2, we get x = 10.
Therefore, the solution to the problem is x = 10.
To solve this problem, let's break it down step-by-step.
Let's assume the number is represented by "x".
Step 1: Express the given information as an equation.
Four times the sum of a number and four is the same as two multiplied by two less than three times the number, can be translated into the equation:
4(x + 4) = 2(3x - 2)
Step 2: Simplify the equation by distributing the factors.
4x + 16 = 6x - 4
Step 3: Collect like terms on one side of the equation.
Subtract 4x from both sides of the equation:
16 = 2x - 4
Step 4: Isolate the variable term.
Add 4 to both sides of the equation:
16 + 4 = 2x
20 = 2x
Step 5: Solve for x.
Divide both sides of the equation by 2:
20/2 = x
x = 10
Therefore, the solution to the problem is x = 10.