QUESTION 3
Easy
If we multiply a number by \( \frac{5}{2} \) and add \( \frac{2}{3} \) to the product, we get \( \frac{−7}{12} \). Find the number.
SOLUTION
1
Assume the number
Let the number be \(x\).
2
Multiply \(x\) by \( \frac{5}{2} \) and add \( \frac{2}{3} \) to the product
After multiplying, we have \( \frac{5}{2} x\)
Now adding \( \frac{2}{3} \) to the product, we get
\( \frac{5}{2} x + \frac{2}{3} = \frac{−7}{12}\)
Now adding \( \frac{2}{3} \) to the product, we get
\( \frac{5}{2} x + \frac{2}{3} = \frac{−7}{12}\)
3
Solve the equation using LCM 12
\( \frac{30x + 8}{12} = \frac{−7}{12}\)
⇒ \(30x + 8 = −7\)
⇒ \(30x = −15\)
⇒ \(x = \frac{−1}{2}\)
⇒ \(30x + 8 = −7\)
⇒ \(30x = −15\)
⇒ \(x = \frac{−1}{2}\)
🏆
Final Answer : The number is \( \frac{−1}{2}\).
Concept Note
Let the number be \(x\) and express the equation using the conditions given. Clear the fractions by multiplying by LCM and find the number(\(x\)).