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### Question 8:
Solve these equations. Check each answer by substituting it back into the equation.

**a.** \(\frac{105}{a} = 5\)

Multiply both sides by \(a\):
\[ 105 = 5a \]

Solve for \(a\):
\[ a = \frac{105}{5} = 21 \]

**b.** \(\frac{3}{b} = 12\)

Multiply both sides by \(b\):
\[ 3 = 12b \]

Solve for \(b\):
\[ b = \frac{3}{12} = \frac{1}{4} \]

**c.** \(\frac{36}{c + 2} = 9\)

Multiply both sides by \(c + 2\):
\[ 36 = 9(c + 2) \]

Expand:
\[ 36 = 9c + 18 \]

Solve for \(c\):
\[ 9c = 36 - 18 \]
\[ 9c = 18 \]
\[ c = \frac{18}{9} = 2 \]

**d.** \(\frac{15}{d - 4} = 25\)

Multiply both sides by \(d - 4\):
\[ 15 = 25(d - 4) \]

Expand:
\[ 15 = 25d - 100 \]

Solve for \(d\):
\[ 25d = 15 + 100 \]
\[ 25d = 115 \]
\[ d = \frac{115}{25} = 4.6 \]

### Question 9:
Two numbers are \(n\) and \(2(n + 3)\).

**a.** The sum of the numbers is 90. Construct an equation.
\[
n + 2(n + 3) = 90
\]

**b.** Solve your equation.

Expand:
\[
n + 2n + 6 = 90
\]
Combine like terms:
\[
3n + 6 = 90
\]
Solve for \(n\):
\[
3n = 90 - 6
\]
\[
3n = 84
\]
\[
n = \frac{84}{3} = 28
\]

**c.** Work out the two numbers.

First number: \(n = 28\)

Second number: \(2(n + 3) = 2(28 + 3) = 2(31) = 62\)

Thus, the two numbers are **28** and **62**.

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### Related Questions:
1. What is the method for solving fractional equations with variables in the denominator?
2. How can you verify if the solutions of an equation are correct?
3. What are the steps to expand and simplify algebraic expressions involving parentheses?
4. How do you solve for two unknowns given their sum?
5. What are some common techniques to handle equations involving multiplication and division?

**Tip:** When solving equations with variables in the denominator, multiplying both sides by the denominator can help eliminate the fraction.

Solve these equations and construct an equation to show the sum of two numbers: n and 2(n + 3), which adds up to 90.

Learn how to solve algebraic equations with variables in the denominator and find two numbers whose sum equals 90. This problem covers key algebraic concepts such as substitution, expansion, and the properties of equality. Suitable for students in Grade 8-9.

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