(a) Divide 34 into two parts in such a way that \[{{\left( \frac{4}{7} \right)}^{th}}\]of one part is equal to \[{{\left( \frac{2}{5} \right)}^{th}}\]of the other. |
(b) Which of the following equation are linear equation in one variable. |
(a) \[{{x}^{2}}+x=1\] |
(b) \[2x-7=\frac{2}{3}\] |
(c) \[{{x}^{2}}+\text{ }x=10~\] |
(d) \[x-15=3x\] |
Answer:
(a) Let, Ist part = x Then, IInd part \[=\left( 34\text{ }-\text{ }x \right)~\] According to question, \[{{\left( \frac{4}{7} \right)}^{th}}\] of Ist part \[{{\left( \frac{2}{5} \right)}^{th}}\] of IInd part or \[\frac{4}{7}x=\frac{2}{5}(34-x)\] or \[20x\text{ }=\text{ }14\left( 34-x \right),\] [by cross multiplication] or \[~20x\text{ }=\text{ }14\text{ }x\text{ }34\text{ }-\text{ }14x\] or \[20x+14x=14\times 34\] or \[34x=14\times 34\] or \[x=\frac{14\times 34}{34}\] or x=14 Hence, two parts are 14 and \[34\text{ }-14\text{ }=\text{ }20\] i.e., 1st part = 14 and Und part = 20 (b) Linear equation in one variable are (c) \[2x-7=\frac{2}{3}\]and(d) \[x-15=3x\]
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