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.
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.
