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Mathematics

Find the value of xx if 4x12+113=5344\dfrac{x}{12} + 1\dfrac{1}{3} = 5\dfrac{3}{4}

Fractions

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Answer

⇒4x12+113=534⇒4x12=534−113⇒4x12=234−43\Rightarrow 4\dfrac{x}{12} + 1\dfrac{1}{3} = 5\dfrac{3}{4}\\[1em] \Rightarrow 4\dfrac{x}{12} = 5\dfrac{3}{4} - 1\dfrac{1}{3}\\[1em] \Rightarrow 4\dfrac{x}{12} = \dfrac{23}{4} - \dfrac{4}{3}

LCM of 4 and 3 = 12.

⇒4x12=23×34×3−4×43×4⇒4x12=6912−1612⇒4x12=69−1612⇒4x12=5312⇒4x12=4512\Rightarrow 4\dfrac{x}{12} = \dfrac{23 \times 3}{4 \times 3} - \dfrac{4 \times 4}{3 \times 4}\\[1em] \Rightarrow 4\dfrac{x}{12} = \dfrac{69}{12} - \dfrac{16}{12}\\[1em] \Rightarrow 4\dfrac{x}{12} = \dfrac{69 - 16}{12}\\[1em] \Rightarrow 4\dfrac{x}{12} = \dfrac{53}{12}\\[1em] \Rightarrow 4\dfrac{x}{12} = 4\dfrac{5}{12}

Comparing both sides, x = 5.

Hence, x = 5.

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