https://file.aiquickdraw.com/mathbot/file/1727423628018kyoxb7d0.jpg

Let's break down the problem step by step to find out how much money Michael had initially.

### Let:
- $ x $ be the amount of money Michael had at first.

### Step 1: Spending on food
- He spent $ \frac{1}{4} $ of his money, i.e., $ \frac{x}{4} $, on food.
- He also spent an additional $30 on food.
- Therefore, after this, the amount left is:

\[
\text{Remaining amount} = x - \left(\frac{x}{4} + 30\right) = x - \frac{x}{4} - 30 = \frac{3x}{4} - 30
\]

### Step 2: Spending on transport
- He then spent $ \frac{2}{5} $ of the remaining money (after food), i.e., $ \frac{2}{5} \times \left( \frac{3x}{4} - 30 \right) $, on transport.
- Additionally, he spent $25 on transport.
- The remaining money after both food and transport is:

\[
\text{Remaining after transport} = \left( \frac{3x}{4} - 30 \right) - \left( \frac{2}{5} \times \left( \frac{3x}{4} - 30 \right) + 25 \right)
\]

This simplifies to:

\[
= \left( \frac{3x}{4} - 30 \right) - \frac{2}{5} \times \left( \frac{3x}{4} - 30 \right) - 25
\]

### Step 3: Final amount left
- We know that after all his spending, Michael had $83 left.
- So, we set the remaining amount equal to 83 and solve for $ x $:

\[
\left( \frac{3x}{4} - 30 \right) - \left( \frac{2}{5} \times \left( \frac{3x}{4} - 30 \right) + 25 \right) = 83
\]

Now I will solve this equation for $ x $.Michael initially had $280.

Would you like further explanation on the steps, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the equation change if Michael had spent $ \frac{1}{3} $ of his money on food instead?
2. What would be the result if the final amount Michael had left was different, say $100?
3. How could you use a different method to verify this solution?
4. What happens if instead of $30 and $25, the amounts spent were proportional to his initial money?
5. How does this problem change if instead of fractions, percentage values are used?

**Tip:** Always translate word problems into mathematical equations step by step to keep track of unknowns and operations clearly.

Michael spent 1/4 of his money and an additional $30 on food. He spent 2/5 of the remaining money and an additional $25 on transport. If Michael had $83 left, how much money did he have at first?

Find out how much money Michael had initially after spending fractions of his money on food and transport, with a detailed step-by-step algebraic solution. This problem involves linear equations and fractions, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation