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What is the algebraic sentence that will help him figure out how many friends he can treat?

Let [tex]f[/tex] be the number of friends.

Click on the correct answer:

A. [tex]\frac{1}{2} f + 10 = 24[/tex]

B. [tex]\frac{1}{2} f - 10 = 24[/tex]

C. [tex]2f + 10 = 24[/tex]

D. [tex]2f - 10 = 24[/tex]

Answer :

To figure out how many friends he can treat, we'll analyze each given algebraic sentence and solve them step-by-step:

1. Sentence 1: [tex]\(\frac{1}{2} f + 10 = 24\)[/tex]

Let's solve for [tex]\( f \)[/tex]:

[tex]\(\frac{1}{2} f + 10 = 24\)[/tex]

Subtract 10 from both sides:

[tex]\(\frac{1}{2} f = 24 - 10\)[/tex]

[tex]\(\frac{1}{2} f = 14\)[/tex]

Multiply both sides by 2 to solve for [tex]\( f \)[/tex]:

[tex]\(f = 14 \times 2\)[/tex]

[tex]\(f = 28\)[/tex]

2. Sentence 2: [tex]\(\frac{1}{2} f - 10 = 24\)[/tex]

Let's solve for [tex]\( f \)[/tex]:

[tex]\(\frac{1}{2} f - 10 = 24\)[/tex]

Add 10 to both sides:

[tex]\(\frac{1}{2} f = 24 + 10\)[/tex]

[tex]\(\frac{1}{2} f = 34\)[/tex]

Multiply both sides by 2 to solve for [tex]\( f \)[/tex]:

[tex]\(f = 34 \times 2\)[/tex]

[tex]\(f = 68\)[/tex]

3. Sentence 3: [tex]\(2 f + 10 = 24\)[/tex]

Let's solve for [tex]\( f \)[/tex]:

[tex]\(2 f + 10 = 24\)[/tex]

Subtract 10 from both sides:

[tex]\(2 f = 24 - 10\)[/tex]

[tex]\(2 f = 14\)[/tex]

Divide both sides by 2 to solve for [tex]\( f \)[/tex]:

[tex]\(f = 14 / 2\)[/tex]

[tex]\(f = 7\)[/tex]

4. Sentence 4: [tex]\(2 f - 10 = 24\)[/tex]

Let's solve for [tex]\( f \)[/tex]:

[tex]\(2 f - 10 = 24\)[/tex]

Add 10 to both sides:

[tex]\(2 f = 24 + 10\)[/tex]

[tex]\(2 f = 34\)[/tex]

Divide both sides by 2 to solve for [tex]\( f \)[/tex]:

[tex]\(f = 34 / 2\)[/tex]

[tex]\(f = 17\)[/tex]

Each solved value for [tex]\( f \)[/tex] gives us the possible number of friends he can treat based on different sentences:

- Sentence 1 results in [tex]\( f = 28 \)[/tex]
- Sentence 2 results in [tex]\( f = 68 \)[/tex]
- Sentence 3 results in [tex]\( f = 7 \)[/tex]
- Sentence 4 results in [tex]\( f = 17 \)[/tex]

Without additional context about the situation, any of these four results could potentially be correct depending on what fits the scenario best.

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