A number is increased by 5 and then multiplied by 3 to give 24. What is the numb

A number is increased by 5 and then multiplied by 3 to give 24. What is the number?

A number is increased by 5 and then multiplied by 3 to give 24. What is the number?

Step 1: Let the unknown number be represented by 'x'.
Step 2: According to the problem, we first increase 'x' by 5. This can be written as 'x + 5'.
Step 3: Next, we multiply the result from Step 2 by 3. This gives us '3(x + 5)'.
Step 4: We know that this result equals 24, so we can write the equation: 3(x + 5) = 24.
Step 5: Now, we simplify the left side of the equation. Distributing 3 gives us: 3x + 15 = 24.
Step 6: To isolate '3x', we need to get rid of the 15. We do this by subtracting 15 from both sides of the equation: 3x + 15 - 15 = 24 - 15.
Step 7: This simplifies to: 3x = 9.
Step 8: Now, we need to find 'x'. We do this by dividing both sides of the equation by 3: 3x / 3 = 9 / 3.
Step 9: This gives us the final answer: x = 3.

Algebraic Manipulation – The question tests the ability to set up and solve a linear equation based on a word problem.
Order of Operations – Understanding the sequence of operations (addition before multiplication) is crucial for correctly forming the equation.