How can I solve math problems faster

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»Basic structure for solving word problems
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Basic structure for solving word problems

Solving word problems will be easier if you follow these steps:

  1. Read the assignment carefully, ideally two or three times.
  2. Make sure you know all of the math terms that appear in the assignment. If you are unsure about a term, you should read it right away or ask someone.
  3. Answer the following questions:
    • What is looking for? This can be a number, for example, or a function equation, or ...
    • What is given Usually there are several different statements in the text.
  4. Try to translate your questions into math notation.
  5. Find a method to solve the problem.
    • Did you get to know a solution procedure for the task type in class?
    • Do you know a formula to calculate the size you are looking for?
    • Can you work out an intermediate result?
  6. Calculate the solution.
  7. If this is possible with this type of exercise: do the test!
  8. Formulate an answer to the question of the task.
An example

The task:
Laura and Vanessa are 28 years old together today. Next year Laura will be twice as old as Vanessa. How old are they today?

What is wanted:

Laura's age in years and Vanessa's age in years.

This is given:

Laura and Vanessa are 28 years old together. In a year Laura will be twice as old as Vanessa.

Translation into a mathematical notation (equations):

There are two unknowns in the task:
\ (L \): Laura's age in years.
\ (V \): Age of Vanessa in years.
We are looking for the values ​​of \ (L \) and \ (V \).

We have to convert the given information into equations that contain the two unknowns. The first equation is simple: The common age of Laura and Vanessa is the sum of the unknowns, our equation is \ (L + V = 28 \). In the second equation, the ages of Laura and Vanessa are in the next year. Then they will be a year older than they are now, i.e. \ (L + 1 \) and \ (V + 1 \). Because Laura will be twice as old as Vanessa, this leads to the equation \ ((L + 1) = 2 \ cdot (V + 1) \).

Solving the equations:

Instructions for solving systems of linear equations can be found here: [Link]
We have to solve the following system of equations: \ begin {align} L + V & = 28 \ (L + 1) & = 2 (V + 1) \ end {align}

Switching from (1) to \ (V \) results in \ (V = 28 - L \). We put that in (2): \ begin {align *} (L + 1) = 2 (28 - L + 1) = 56 - 2L +2. \ End {align *} From this we can \ (L \) to calculate:

 

\ begin {align *} L + 1 & = 56 -2L + 2 \ tag * {| + 2L} \ 3L + 1 & = 56 + 2 \ tag * {| - 1} \ 3L & = 57 \ tag * {|: 3} \ L & = \ frac {57} {3} = 19 \ end {align *}

 

Inserting in (1) yields \ (V = 28 - L = 28 - 19 = 9 \).

Do the test:

This year Laura and Vanessa are together \ (19 + 9 = 28 \) years old. Next year Laura will be 20 and Vanessa will be 10, so Laura is twice as old as Vanessa.

Answer sentence:

Laura is 19 years old and Vanessa is 9 years old.