Unit 2 - Objective 6 - Translating Words into Mathematic Expressions and Solving


Most problems you have to solve at work will be word problems.   Once you have written equations, the most difficult part is over.  All that is left is to solve the equation and check your answers.

Suggestions for solving word problems:

  1. Read the problem carefully.
  2. Make a sketch if possible.
  3. Clearly identify the unknown quantities.
  4. If possible, represent all the unknowns in terms of just one variable..
  5. Analyze the problem carefully. Write the equation relating the variables.
  6. Solve the equation.
  7. Check your answer.
  8. Be sure you answered the original question.
Examples:
1. One printer can complete a certain job in 3 hours.   Another printer can do the same job in 2 hours.  How long will it take if both printers work on the job?

Solution:
Let x = the number of hours it takes both machines to complete the job.
In one hour the two machines can complete 1/x of the job.
The first printer does 1/3 of the job in 1 hour when it works alone.
The second printer does 1/2 of the job in1 hour when it works alone.

Together:

1/x = 1/3 + 1/2
(get a LCD which is 6x)
6x (1/x) = (1/3 + 1/2) 6x
6 = 2x + 3x
6 = 5x
x = 6/5

So together they can complete the job in 6/5 hours or 1 hours 12 minutes.

2. A batch of steel containing 5% nickel and 95% iron is combined with another batch having 2% nickel and 98% iron, to make 3 tons of steel having 4% nickel and 96% iron.  How many tons of each original batch is needed?

Solution:
Let x = the number of tons of 5% steel needed.
3 - x = the number of tons of 2% steel needed.
(x + (3 - x)) = 3 tons which is the total amount needed. Write an equation for the amount of nickel.

(5% of x tons)+(2% of (3-x) tons) = (4% of 3 tons)

5%x + 2% (3 - x) = 4% (3)
.05x + .02 (3 - x) = .04 (3)
(multiply by 100)
5x + 2 (3 - x) = 4 (3)
5x + 6 - 2x = 12
3x + 6 = 12
3x = 6
x = 2

x = 2 tons of 5% steel.
3 - x = 3 - 2 = 1 ton of 2% steel.


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