Andy received $160 for his birthday this year. This was $30 less than one-half the amount he received last year. Which equation, when solved for x, gives the amount Andy received for his birthday last year?

Answer 1

Let's denote the amount Andy received last year as \( x \).

According to the problem, one-half of the amount he received last year would be \( \frac{x}{2} \).

The problem states that Andy received $160 this year, and that amount was $30 less than one-half of what he received last year. Therefore, we can express this relationship with the following equation:

\[ \frac{x}{2} - 30 = 160 \]

This equation represents the situation described.

To solve for \( x \), you can first isolate \( \frac{x}{2} \):

1. Add 30 to both sides: \[ \frac{x}{2} = 160 + 30 \] \[ \frac{x}{2} = 190 \]

2. Multiply both sides by 2 to solve for \( x \): \[ x = 190 \times 2 \] \[ x = 380 \]

So, the amount Andy received last year was $380.

To summarize, the equation you are looking for is:

\[ \frac{x}{2} - 30 = 160 \]