Linear Equation...

In a shooting competition a marksman receives $$50$$ paise if he hits the mark and pays $$20$$ paise if he misses it. He tried $$60$$ shots and was paid Rs. $$1.30$$. How many times did he hit the mark?

If $$\displaystyle x=m+1$$ and $$\displaystyle \frac{1}{3}(6x-3)-(8-3x)=11;$$ find the value of $$m$$.

The angles of a triangle are $$2\left ( x-7 \right )$$ , $$\displaystyle \frac{3}{2}\left ( x-1 \right )$$ and $$3\left ( x+11 \right )$$ . Find $$x$$ and then show that the triangle is isosceles.

If the sum of three consecutive integers is $$63$$. Find the smallest number.

Solve: $$8x+\displaystyle \frac{21}{4}= 3x+7$$ , then $$x=$$

Some part of a journey of $$555\ km$$ was completed by a car with speed $$60\ km/h$$. Then the speed is increased by $$15\ km/h$$ and the journey is completed. If it takes $$8$$ hours to reach, find the time taken by $$60\ km/h$$ speed.

The measures of the angles of a triangle are $$2x,x+25$$ and $$3x+5$$. Find $$x$$ and then show that the triangle is isosceles.

A boy has $$x$$ coins of $$50$$ paise each$$,\: 2x$$ coins of $$25$$ paise each, $$4x$$ coins of $$10$$ paise each and $$8x$$ coins of $$5$$ paise each. Find the number of $$5$$ paise coins if the value of all the coins is Rs. $$9$$.

The difference between $$ \displaystyle \frac{3}{4} $$ of a line and $$ \displaystyle \frac{2}{5} $$ of the same line is $$28$$ cm. Find the length of the line.

If $$(2ax + 1) (3x + 1) = 6a (x + 1)$$ and $$x = 1$$, find the value of $$a$$.