System Analysis

Explanation

Analyze

• If the number of calls increases by 350, the system will reach capacity (Given)
• The maximum capacity of the system is 1500 calls per hour. (Given)
• How many calls are currently being made each hour? (find)

Caution! Unlike an arithmetic approach, you do not have to determine whether to add, subtract, multiply, or divide at this stage.  Simply translate the words of the problem to mathematical symbols to form an equation that describe the situation.  Then solve the equation.

Form

Let n = the number of calls currently being made each hour.  To form an equation involving n, we look for a key word or phrase in the problem.

key phrase: increase by 350

Translation: addition

The key phrase tells us to add 350 to the current number of calls to obtain an expression for the maximum capacity of the system.  Now we translate the words of the problem into an equation.

• (The current number of calls per hour) increased by (350) equals (the maximum capacity of the system)
• n + 350 = 1500

Solve

• We need to isolate n on the left side
  • n + 350  1500
• To isolate n, subtract 350 from both sides to undo the addition of 350
  • n  + 350 - 350 = 1500 - 350
• Do the subtraction
  • n = 1150

State

Currently, 1150 calls per hour are being made

Check

if the number of calls currently being made each hour is 1150 and we increase that number by 350, we should obtain the maximum capacity of the system.

The result, 1150, checks

Caution! Always check the result in the original wording of the problem, not by substituting it into the equation.  Why? The equation may have been solved correctly, but the danger is that you may have formed it incorrectly.