question_answer

(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) \[x-15=3x\]