To determine which situations can represent the expression [tex]\( 6 - \chi \)[/tex], let's analyze each situation step by step:
1. Naomi gives some of her six pencils away.
- Naomi starts with 6 pencils. If she gives away some pencils, the number of pencils she has left is 6 minus some amount, [tex]\(\chi\)[/tex].
- Therefore, this can be represented by [tex]\( 6 - \chi \)[/tex].
2. Sydney increased her collection of coins by six.
- Sydney's collection of coins increased by 6. This is an addition, not a subtraction.
- Therefore, this cannot be represented by [tex]\( 6 - \chi \)[/tex].
3. Benjamin lost six of his stickers.
- Benjamin lost exactly 6 stickers, meaning the reduction is a fixed number (6), not a variable amount.
- Therefore, this cannot be represented by [tex]\( 6 - \chi \)[/tex].
4. Six servings of dinner were decreased by a number.
- There are 6 servings of dinner, and if the number of servings is decreased by a variable amount, [tex]\(\chi\)[/tex], it can be represented as [tex]\( 6 - \chi \)[/tex].
- Therefore, this can be represented by [tex]\( 6 - \chi \)[/tex].
5. Westville has 6 fewer schools than Eastville.
- This situation describes a difference between two fixed amounts (the number of schools in Westville and Eastville), specifically 6 fewer schools.
- Therefore, this cannot be represented by [tex]\( 6 - \chi \)[/tex].
6. Gabrielle decreased her 6 -minute mile by an unknown amount of time.
- If Gabrielle's 6-minute mile time is reduced by an unknown amount, [tex]\(\chi\)[/tex], it can be written as [tex]\( 6 - \chi \)[/tex].
- Therefore, this can be represented by [tex]\( 6 - \chi \)[/tex].
Thus, the situations that can be represented by the expression [tex]\( 6 - \chi \)[/tex] are:
1. Naomi gives some of her six pencils away.
4. Six servings of dinner were decreased by a number.
6. Gabrielle decreased her 6-minute mile by an unknown amount of time.
So the correct answer is:
[1, 4, 6]
