George spent 25% of the money he had on lunch and 60% of the remaining money on dinner. If he then had $9.00 left, how much money did he spend on lunch and dinner?

Options

A. `$19`
B. `$20`
C. `$21`
D. `$27`

Answer

Let's solve the problem step by step.

### Step 1: Define the initial amount of money
Let \( x \) be the initial amount of money George had.

### Step 2: Calculate the amount spent on lunch
George spent 25% of his initial money on lunch. This can be calculated as:
\[ \text{Money spent on lunch} = 25\% \text{ of } x = \frac{25}{100} \times x = \frac{1}{4}x \]

### Step 3: Calculate the remaining money after lunch
After spending on lunch, the remaining money is:
\[ \text{Remaining money} = x - \frac{1}{4}x = \frac{3}{4}x \]

### Step 4: Calculate the amount spent on dinner
George then spent 60% of the remaining money on dinner. The amount spent on dinner can be calculated as:
\[ \text{Money spent on dinner} = 60\% \text{ of remaining money} = 60\% \text{ of } \frac{3}{4}x = \frac{60}{100} \times \frac{3}{4}x = \frac{3}{5} \times \frac{3}{4}x = \frac{9}{20}x \]

### Step 5: Calculate the remaining money after dinner
After spending on dinner, the remaining money is:
\[ \text{Remaining money} = \frac{3}{4}x - \frac{9}{20}x \]
To perform this subtraction, we need a common denominator. The least common multiple of 4 and 20 is 20. Therefore, we convert \(\frac{3}{4}x\) to have a denominator of 20:
\[ \frac{3}{4}x = \frac{15}{20}x \]
Now we can subtract:
\[ \text{Remaining money} = \frac{15}{20}x - \frac{9}{20}x = \frac{6}{20}x = \frac{3}{10}x \]

### Step 6: Set up the equation based on the remaining money
According to the problem, George had $9 left after lunch and dinner:
\[ \frac{3}{10}x = 9 \]

### Step 7: Solve for \( x \)
To find \( x \), we multiply both sides of the equation by \(\frac{10}{3}\):
\[ x = 9 \times \frac{10}{3} = 30 \]
Thus, George initially had $30.

### Step 8: Calculate the total amount spent on lunch and dinner
Now we can calculate the amounts spent on lunch and dinner:
- Money spent on lunch:
\[ \text{Lunch} = \frac{1}{4}x = \frac{1}{4} \times 30 = 7.5 \]
- Money spent on dinner:
\[ \text{Dinner} = \frac{9}{20}x = \frac{9}{20} \times 30 = 13.5 \]

### Step 9: Total money spent
Now, we add the amounts spent on lunch and dinner:
\[ \text{Total spent} = 7.5 + 13.5 = 21 \]

### Final Answer
George spent a total of $21 on lunch and dinner.

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