Math Problem Statement

Bobs pay increased by 5% to $315 so what was his original pay?

Solution

To find Bob's original pay before the 5% increase, we can set up the equation as follows:

Let xx represent Bob's original pay. After the 5% increase, his new pay is $315. This means his original pay plus 5% of his original pay equals $315:

x+0.05x=315x + 0.05x = 315

This simplifies to:

1.05x=3151.05x = 315

Now, solve for xx:

x=3151.05x = \frac{315}{1.05}

x=300x = 300

So, Bob's original pay was $300.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

  1. What would Bob's pay be if his pay increased by 10% instead of 5%?
  2. If Bob's pay decreased by 5%, what would his new pay be?
  3. How much did Bob's pay increase in actual dollars?
  4. If Bob's pay increased to $400 after a 5% raise, what was his original pay?
  5. What would Bob's original pay be if the final amount was $315 after a 7% increase?

Tip: When solving percentage problems, it's often easier to convert percentages to decimals (e.g., 5% = 0.05) for use in equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Percentages

Formulas

New Pay = Original Pay + (Percentage Increase * Original Pay)
Original Pay = New Pay / (1 + Percentage Increase)

Theorems

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Suitable Grade Level

Grades 6-8