Question

Which set of algebra tiles represents the sentence below?

Ada drove 2 fewer miles today than she drove yesterday.
2 boxes contain negative x and 1 box contains a plus sign.

1 box contains x and 2 boxes contain a minus sign.

1 box contains negative x and 2 boxes contain plus signs.

2 boxes contain x and 1 box contains a minus sign.

Answer 1

To represent the sentence "Ada drove 2 fewer miles today than she drove yesterday," we can break it down mathematically.

Let \( x \) represent the number of miles Ada drove yesterday. According to the sentence, today she drove 2 miles less than yesterday. This can be expressed as:

\[
x - 2
\]

In terms of algebra tiles:
- The \( x \) represents the miles driven yesterday.
- The "fewer 2" means we are subtracting 2 from \( x \).

Let's analyze the options:

1. **2 boxes contain negative x and 1 box contains a plus sign**: This suggests a representation of \(-2x + 1\). This does not match our equation.

2. **1 box contains x and 2 boxes contain a minus sign**: This represents \( x - 2 \), which exactly matches the equation we derived.

3. **1 box contains negative x and 2 boxes contain plus signs**: This represents \(-x + 2\), which does not match.

4. **2 boxes contain x and 1 box contains a minus sign**: This represents \( 2x - 1\), which does not match.

Therefore, the correct set of algebra tiles that represents "Ada drove 2 fewer miles today than she drove yesterday" is:

**1 box contains x and 2 boxes contain a minus sign**.