Question

Six persons decided to donate money to three beggars equally. The first five have the same amount of money, while the sixth has $\$1.$ If each beggar gets $\$7,$ then how much money does each of the five friends have ?.
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Answer 1

Let each of the five friends have the amount of money be $\$x.$
A sum of money with five friends $=5x$
A money with the sixth person = $\$1$
Total money donated by six friends $=5x+1$

If $5x+1$ amount of money is divided among 3 beggars, then each beggar gets $\$7.$
$\therefore \frac{(5x+1)}{3}=7.$

Step 1: Multiply both the sides by 3
$\frac{(5x+1)}{3}\times 3=7\times 3$
$\Rightarrow (5x+1)=21$

Step 2: Subtract both sides of the equation by 1 to eliminate 1 on the left side of the equation.
$\Rightarrow 5x+1-1=21-1\Rightarrow 5x=20$

Step 3: Now, divide both sides by 5 to eliminate 5 on the left side of the equation.
$\Rightarrow \frac{5x}{5}=\frac{20}{5}\Rightarrow \frac{5\times x}{5}=\frac{5\times 4}{5}\Rightarrow x=4$

Hence, each of the five friends have $\$4.$