Mei Feng spent 20% of her money on a shirt. She used the rest of the money to buy a bag and a necklace. The bag cost $24 more than the shirt. The necklace cost $72. Find the cost of the bag.

Let the total amount of money Mei Feng had initially be $ x $.

### Step 1: Cost of the shirt
She spent 20% of her money on the shirt, so the cost of the shirt is:
\[
\text{Cost of shirt} = 0.2x
\]

### Step 2: Remaining money after buying the shirt
After buying the shirt, she has $ 80\% $ of her money left:
\[
\text{Remaining money} = 0.8x
\]

### Step 3: Set up the equation for the remaining money
She used this remaining money to buy the bag and the necklace. The cost of the bag is $24 more than the cost of the shirt, so the cost of the bag is:
\[
\text{Cost of bag} = 0.2x + 24
\]

The cost of the necklace is $72, so the total amount she spent on the bag and the necklace is equal to the remaining money:
\[
(0.2x + 24) + 72 = 0.8x
\]

### Step 4: Solve for $ x $
Simplify the equation:
\[
0.2x + 96 = 0.8x
\]
Subtract $ 0.2x $ from both sides:
\[
96 = 0.6x
\]
Solve for $ x $:
\[
x = \frac{96}{0.6} = 160
\]

### Step 5: Find the cost of the bag
The cost of the shirt is $ 0.2 \times 160 = 32 $, so the cost of the bag is:
\[
\text{Cost of bag} = 32 + 24 = 56
\]

Thus, the cost of the bag is **$56**.

Would you like more details on any part? Here are five related questions:

1. How would the solution change if the necklace cost more?
2. What if Mei Feng spent 30% of her money on the shirt?
3. How can you verify that the solution is correct?
4. What if the bag cost less than the shirt?
5. How does changing the percentage spent on the shirt affect the final answer?

**Tip:** Always break down the problem into parts and define variables clearly. This makes solving complex word problems easier.

Solve this algebra word problem where Mei Feng spends 20% of her money on a shirt, and the bag costs $24 more than the shirt. The necklace costs $72. Find out the cost of the bag using percentages and linear equations. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation