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2. To support a local senior citizens center, a student club sent a flyer home to the [tex]$n$[/tex] students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise [tex]$T$[/tex] dollars. Match each quantity to an expression, an equation, or an inequality that describes it.

A. The dollar amount the club would have if they reached half of their goal:
1. [tex]$0.5 T$[/tex]

B. The dollar amount the club would have if every student at the school donated 50 cents to the cause:
2. [tex]$0.5 n$[/tex]

C. The dollar amount the club could donate if they made [tex]$\$[/tex] 50[tex]$ more than their goal:
3. $[/tex]T + 50[tex]$

D. The dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents:
4. $[/tex]T - 0.5 n[tex]$

E. The dollar amount the club would have if half of the students at the school each gave 50 cents:
5. $[/tex]0.25 n$



Answer :

GinnyAnswer
Sure, I'll guide you step-by-step to match each scenario with the corresponding expression. Let's assess each part carefully.

### Analyzing Each Quantity

1. A: The dollar amount the club would have if they reached half of their goal.
- If the goal is [tex]\( T \)[/tex] dollars, then half of it would be [tex]\( 0.5T \)[/tex].

2. B: The dollar amount the club would have if every student at the school donated 50 cents to the cause.
- If each of the [tex]\( n \)[/tex] students donated 50 cents (which is equivalent to [tex]$0.5), then the amount collected would be \( 0.5n \). 3. C: The dollar amount the club could donate if they made $[/tex]50 more than their goal.
- If they raised [tex]$50 more than their goal of \( T \) dollars, the total amount would be \( T + 50 \). 4. D: The dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents. - If each of the \( n \) students donated 50 cents, the total collected would be \( 0.5n \). Therefore, the amount still needed to reach the goal \( T \) would be \( T - 0.5n \). 5. E: The dollar amount the club would have if half of the students at the school each gave 50 cents. - Half of the \( n \) students are \( 0.5n \). If each of these students gave 50 cents, the amount collected would be \( 0.5 \times 0.5n = 0.25n \). ### Matching Each Quantity Based on the analysis, here are the correct matches: A. \( 0.5T \) - the dollar amount the club would have if they reached half of their goal B. \( 0.5n \) - the dollar amount the club would have if every student at the school donated 50 cents to the cause C. \( T + 50 \) - the dollar amount the club could donate if they made $[/tex]50 more than their goal
D. [tex]\( T - 0.5n \)[/tex] - the dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents
E. [tex]\( 0.25n \)[/tex] - the dollar amount the club would have if half of the students at the school each gave 50 cents

### Final Solution

1. [tex]\( 0.5T \)[/tex] - Reached half of their goal ([tex]\(A\)[/tex])
2. [tex]\( 0.5n \)[/tex] - Every student donated 50 cents ([tex]\(B\)[/tex])
3. [tex]\( T + 50 \)[/tex] - Made $50 more than their goal ([tex]\(C\)[/tex])
4. [tex]\( T - 0.5n \)[/tex] - Still need to raise to reach its goal after donations ([tex]\(D\)[/tex])
5. [tex]\( 0.25n \)[/tex] - Half of the students each gave 50 cents ([tex]\(E\)[/tex])