Greg spent 1/4 of his money on a typewriter and 2/3 of the remainder on a gift.
(a)  If the typewriter cost$120, how much did he have at first?

Use casco mathematics tutor primary 6A

Let's solve the problem step by step using basic algebra.

### Given:
1. Greg spent $ \frac{1}{4} $ of his money on a typewriter.
2. The typewriter cost $120.
3. Greg then spent $ \frac{2}{3} $ of the remaining money on a gift.

### To Find:
- How much money did Greg have initially?

### Steps to Solve:

1. **Let the initial amount of money Greg had be $ x $.**
   
2. **Greg spent $ \frac{1}{4} $ of his money on the typewriter:**
   \[
   \text{Cost of the typewriter} = \frac{1}{4}x = 120
   \]

3. **Solve for $ x $:**
   \[
   \frac{1}{4}x = 120
   \]
   Multiply both sides by 4 to get:
   \[
   x = 120 \times 4 = 480
   \]
   So, Greg initially had $480.

### Answer:
Greg had $480 at first.

Would you like more details on this solution or have any questions?

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Here are five related questions for further practice:

1. If Greg had spent $ \frac{1}{3} $ of his remaining money on another item, how much would he have left?
2. How much money did Greg spend in total after buying the typewriter and the gift?
3. If the typewriter cost $150 instead, how much money would Greg have initially?
4. What fraction of Greg's initial money did he have left after buying both the typewriter and the gift?
5. If Greg had $600 initially, how much would the typewriter cost if he spent $ \frac{1}{4} $ of his money on it?

**Tip:** When dealing with fractions of an amount, it's often helpful to set up an equation to represent the relationships clearly.

Learn how to calculate Greg's initial amount of money using fractional arithmetic. This problem involves solving a word problem where Greg spends fractions of his money on a typewriter and a gift. Suitable for Primary 6A students.

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