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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