Solve for the variables in these simple algebra problems.

Let's solve each problem step by step.

---

Problem 1:

$$
8 + \frac{35}{w} = 15
$$

#### Step 1: Isolate the fraction.
Subtract 8 from both sides:
$$
\frac{35}{w} = 15 - 8
$$
$$
\frac{35}{w} = 7
$$

#### Step 2: Solve for \( w \).
Multiply both sides by \( w \):
$$
35 = 7w
$$
Divide both sides by 7:
$$
w = \frac{35}{7} = 5
$$

#### Final Answer:
$$
\boxed{d}
$$

---

Problem 2:

$$
5 = \frac{s}{8} - 3
$$

#### Step 1: Isolate the fraction.
Add 3 to both sides:
$$
5 + 3 = \frac{s}{8}
$$
$$
8 = \frac{s}{8}
$$

#### Step 2: Solve for \( s \).
Multiply both sides by 8:
$$
s = 8 \times 8 = 64
$$

#### Final Answer:
$$
\boxed{c}
$$

---

Problem 3:

$$
6 = \frac{27}{n} - 3
$$

#### Step 1: Isolate the fraction.
Add 3 to both sides:
$$
6 + 3 = \frac{27}{n}
$$
$$
9 = \frac{27}{n}
$$

#### Step 2: Solve for \( n \).
Multiply both sides by \( n \):
$$
9n = 27
$$
Divide both sides by 9:
$$
n = \frac{27}{9} = 3
$$

#### Final Answer:
$$
\boxed{b}
$$

---

Problem 4:

$$
11 + \frac{72}{z} = 20
$$

#### Step 1: Isolate the fraction.
Subtract 11 from both sides:
$$
\frac{72}{z} = 20 - 11
$$
$$
\frac{72}{z} = 9
$$

#### Step 2: Solve for \( z \).
Multiply both sides by \( z \):
$$
72 = 9z
$$
Divide both sides by 9:
$$
z = \frac{72}{9} = 8
$$

#### Final Answer:
$$
\boxed{d}
$$

---

Problem 5:

$$
10 = \frac{s}{7} - 1
$$

#### Step 1: Isolate the fraction.
Add 1 to both sides:
$$
10 + 1 = \frac{s}{7}
$$
$$
11 = \frac{s}{7}
$$

#### Step 2: Solve for \( s \).
Multiply both sides by 7:
$$
s = 11 \times 7 = 77
$$

#### Final Answer:
$$
\boxed{c}
$$

---

Problem 6:

$$
5y - 15 = 60
$$

#### Step 1: Isolate the term with \( y \).
Add 15 to both sides:
$$
5y = 60 + 15
$$
$$
5y = 75
$$

#### Step 2: Solve for \( y \).
Divide both sides by 5:
$$
y = \frac{75}{5} = 15
$$

#### Final Answer:
$$
\boxed{d}
$$

---

Problem 7:

$$
101 = 5 + 4x
$$

#### Step 1: Isolate the term with \( x \).
Subtract 5 from both sides:
$$
101 - 5 = 4x
$$
$$
96 = 4x
$$

#### Step 2: Solve for \( x \).
Divide both sides by 4:
$$
x = \frac{96}{4} = 24
$$

#### Final Answer:
$$
\boxed{b}
$$

---

Problem 8:

$$
\frac{87}{y} - 10 = 19
$$

#### Step 1: Isolate the fraction.
Add 10 to both sides:
$$
\frac{87}{y} = 19 + 10
$$
$$
\frac{87}{y} = 29
$$

#### Step 2: Solve for \( y \).
Multiply both sides by \( y \):
$$
87 = 29y
$$
Divide both sides by 29:
$$
y = \frac{87}{29} = 3
$$

#### Final Answer:
$$
\boxed{b}
$$

---

Problem 9:

$$
66 + n - 17 = 76
$$

#### Step 1: Simplify the left-hand side.
Combine like terms:
$$
66 - 17 + n = 76
$$
$$
49 + n = 76
$$

#### Step 2: Solve for \( n \).
Subtract 49 from both sides:
$$
n = 76 - 49
$$
$$
n = 27
$$

#### Final Answer:
$$
\boxed{d}
$$

---

Problem 10:

$$
3 + \frac{50}{s} = 28
$$

#### Step 1: Isolate the fraction.
Subtract 3 from both sides:
$$
\frac{50}{s} = 28 - 3
$$
$$
\frac{50}{s} = 25
$$

#### Step 2: Solve for \( s \).
Multiply both sides by \( s \):
$$
50 = 25s
$$
Divide both sides by 25:
$$
s = \frac{50}{25} = 2
$$

#### Final Answer:
$$
\boxed{c}
$$

---

Final Answers:

1. \( \boxed{d} \)
2. \( \boxed{c} \)
3. \( \boxed{b} \)
4. \( \boxed{d} \)
5. \( \boxed{c} \)
6. \( \boxed{d} \)
7. \( \boxed{b} \)
8. \( \boxed{b} \)
9. \( \boxed{d} \)
10. \( \boxed{c} \)