You must first set up a revenue equation where $\displaystyle a$ represents the number of bunches of apples sold and $\displaystyle w$ represents the number of watermelons sold.  

This would give us the equation 

$\displaystyle 5a+3w=r$.  

The problem gives us both $\displaystyle w$ and $\displaystyle r$ and when we plug those values in we get 

$\displaystyle 5a+3(10)=100$ 

or

$\displaystyle 5a+30=100$.

Now you must get $\displaystyle a$ by itself.  

First, subtract $\displaystyle 30$ from both sides leaving $\displaystyle 5a=70$.  

Then divide both sides by $\displaystyle 5$ to get your answer $\displaystyle a=14$.

To solve this algebraic word problem, first set up an equation:

$\displaystyle x + (x-8) = 60$

The variable $\displaystyle x$ represents the amount of people in the group.

Add $\displaystyle x + x = 2x$

$\displaystyle 2x - 8 = 60$

Isolate the variable by adding 8 to both sides of the equation:

$\displaystyle 2x - 8 + 8 = 60+8$

$\displaystyle 2x = 68$

$\displaystyle x = 34$

$\displaystyle (x-8) = 34-8$

$\displaystyle x = 26$

Check to make sure that the two conditions of the problem have been met.

Condition one: The two numbers added together must equal 60.

$\displaystyle 34 + 26 = 60$

Condition two. One of the numbers is eight less than the other.

$\displaystyle 34-26 = 8.$

Because these two conditions have been met, there are $\displaystyle 34$ people in one group and $\displaystyle 26$ people in the second group.

The formula for computing the area of a rectangle is Area = l x w, where l = length and w = width.

In this algebraic word problem, let the variable $\displaystyle x$ represent the length and $\displaystyle (x-5)$ will represent the width of the rectangle.

Write an equation:

$\displaystyle x (x-5) = 36cm$

Distribute the variable $\displaystyle x$ to what is inside the parentheses:

$\displaystyle x^{2} -5x = 36$

Set that expression equal to zero by subtracting 36 from both sides:

$\displaystyle x^{2} - 5x -36 = 0$

Factor using the FOIL Method:

$\displaystyle (x-9) (x+4) = 0$

Set each equal to zero to find the values of x that make this expression true:

$\displaystyle (x-9) = 0$

$\displaystyle x = 9$

$\displaystyle (x+4) = 0$

$\displaystyle x = -4$

There are two possible values for $\displaystyle x$; $\displaystyle x = 9$ and $\displaystyle x = -4$

Because a dimension cannot be a negative integer, reject $\displaystyle x = -4.$ Therefore $\displaystyle x = 9$. This is the measurement of the length of the rectangle.

$\displaystyle (x-5) = 9-5 = 4$

$\displaystyle 4$ represents the width of the rectangle.

Now check to see if the two conditions are met.

Condition 1: Area = length x width

$\displaystyle 9 x 4 = 36cm$

Condition 2: The width is 5cm less than the length.

$\displaystyle 9 -5 =4cm$

Therefore $\displaystyle 9cm$ is the length and $\displaystyle 4cm$ is the width of this rectangle.