A number is divided by 2 and then increased by 3. The result is 10. What is the

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Question: A number is divided by 2 and then increased by 3. The result is 10. What is the number?

Options:

Correct Answer: 14

Solution:

Let the number be x. Then, x/2 + 3 = 10. Subtracting 3 from both sides gives x/2 = 7. Multiplying by 2 gives x = 14.

A number is divided by 2 and then increased by 3. The result is 10. What is the number?

A number is divided by 2 and then increased by 3. The result is 10. What is the number?

Step 1: Let the unknown number be represented by 'x'.
Step 2: According to the problem, when 'x' is divided by 2, we write it as 'x/2'.
Step 3: After dividing by 2, we increase the result by 3, which we write as 'x/2 + 3'.
Step 4: We know that this result equals 10, so we can write the equation: x/2 + 3 = 10.
Step 5: To solve for 'x', we first need to get rid of the +3. We do this by subtracting 3 from both sides of the equation.
Step 6: This gives us the new equation: x/2 = 10 - 3, which simplifies to x/2 = 7.
Step 7: Now, we need to get 'x' by itself. We do this by multiplying both sides of the equation by 2.
Step 8: This gives us: x = 7 * 2, which simplifies to x = 14.
Step 9: Therefore, the number we are looking for is 14.

Algebraic Manipulation – The question tests the ability to set up and solve a simple algebraic equation based on a verbal problem.
Order of Operations – Understanding the sequence of operations (division, addition) is crucial to correctly interpreting the problem.