WRITING A REAL WORLD SITUATION FROM AN EQUATION

An equation with the variable on both sides can be used to represent a real-world situation. We can reverse this process by writing a real-world situation for a given equation.

Example 1 :

Write a real-world situation that could be modeled by the equation 55x = 150 + 25x.

Solution :

Step 1 : 

The left side of the equation consists of a variable term. It could represent the cost for doing the same job on hourly basis.

That is, $55 is charged per hour for doing some job and 55x represents the total cost for  doing the same job for 'x' hours. 

Step 2 : 

The right side of the equation consists of a constant plus a variable term. It could represent the total cost for doing a job where there is an initial fee plus an hourly charge. 

That is, an initial fee $150 plus an hourly charge of 25$. And 150 + 25x represents the total cost for doing the job for 'x' hours. 

Step 3 : 

The equation 55x  =  150 + 25x could be represented by this situation :

Jose is a painter and he charges $55 per hour for house painting. Alex is also a painter and he charges $150 plus $25 per hour.

The equation 55x = 150 + 25x tells us for how many hours the total cost charged by both of them would be same.

or 

The total cost charged by both of them would be same for 'x' number of hours.

Example 2 :

Write a real-world situation that could be modeled by the equation 20 + 30x = 36 + 28x.

Solution :

Step 1 : 

The left side of the equation consists of a constant plus a variable term. It could represent that there was some water in a can initially and water is being filled in the can.  

That is, initially there was 20 liters of water in the can and now 30 liters of water is filled per hour. And 20 + 30x represents the total amount of water in the can after 'x' hours. 

Step 2 : 

The right side of the equation consists of a constant plus a variable term. It could represent that there was some water in a can initially and water is being filled in the can.  

That is, initially there was 36 liters of water in the can and now 28 liters of water is filled per hour. And 36 + 28x represents the total amount of water in the can after 'x' hours. 

Step 3 : 

The equation 20 + 30x  =  36 + 28x could be represented by this situation :

A can had 20 liters of water initially and it is being filled by water at the rate of 30 liters per hour. Another can had 36 liters of water initially and it is being filled by water at the rate of 28 liters per hour

The equation 20 + 30x  =  36 + 28x tells us after how many hours the total amount of water in both the cans would be same.

or 

The total amount of water in both the cans would be same after 'x' hours.

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