#### Topic Content:

- Word Problems Leading to Simple Linear Equations

### Worked Example 9.2.1:

Solve the following:**i. **If three-quarters of a certain number is 10 more than one-third of the number what is the number.**ii.** A man spends one-third of his monthly salary earning on projects and one-quarter of the remainder on household needs. If he has N15000 left how much does he receive in a month?**iii.** Think of a number, treble it, then divide by 4, the result is 12 more than the original number, find the number.** iv. **When 12 is subtracted from a number, and the answer is divided into 10, the result obtained is one-quarter of the original number. Find the number.

**v.**A mother is four times as old as her daughter. If their age difference is three decades, find the ages of the mother and her daughter.

**i. **If three-quarters of a certain number is 10 more than one-third of the number what is the number?

**Solution**

Let the number be x

⇒ \( \frac{3}{4}\scriptsize x = 10 \: +\: \normalsize \frac{1}{3}\scriptsize x \)

**Take L.C.M**

⇒ \( \frac{3x}{4} \: + \: \frac{1x}{3} \)

**Cross multiply**

⇒ \( \scriptsize 3x \: \times \: 3 = 4(30 \: + \: x) \)

⇒ \( \scriptsize 9x = 120 \: + \: 4x \)

**Take like terms**

⇒ \( \scriptsize 9x \: – \:4x = 120 \)

⇒ \( \scriptsize 5x = 120 \)

**Divide both sides by 5**

⇒ \( \frac{ 5x}{5} = \frac{120}{5} \)

⇒ \( \frac{ \not{5}x}{\not{5}} = \frac{120}{5} \)

\( \scriptsize x = 24 \)

**ii.** A man spends one-third of his monthly salary earning on projects and one-quarter of the remainder on household needs. If he has N15000 left how much does he receive in a month?

**Solution**

**Let the income be x**

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