A number is tripled and then increased by 2 to equal 20. What is the number?

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Question: A number is tripled and then increased by 2 to equal 20. What is the number?

Options:

Correct Answer: 6

Solution:

Let the number be x. The equation is 3x + 2 = 20. Subtracting 2 gives 3x = 18, so x = 6.

A number is tripled and then increased by 2 to equal 20. What is the number?

A number is tripled and then increased by 2 to equal 20. What is the number?

Step 1: Let the unknown number be represented by the letter 'x'.
Step 2: According to the problem, when the number is tripled, it becomes '3x'.
Step 3: After tripling the number, we add 2 to it, which gives us '3x + 2'.
Step 4: We know that this result equals 20, so we can write the equation: 3x + 2 = 20.
Step 5: To solve for 'x', we first need to get rid of the +2. We do this by subtracting 2 from both sides of the equation: 3x + 2 - 2 = 20 - 2.
Step 6: This simplifies to: 3x = 18.
Step 7: Now, we need to find 'x'. We do this by dividing both sides of the equation by 3: 3x / 3 = 18 / 3.
Step 8: This simplifies to: x = 6.

Algebraic Equations – The question tests the ability to set up and solve a linear equation based on a verbal problem.
Order of Operations – Understanding the sequence of operations (tripling, then adding) is crucial for forming the correct equation.