Basics of Word Problems

You MUST know how to translate basic phrases!

Read the problem once to decide what you are asked to find.

Write down what you are looking for and how you will represent it with a variable:

*If there is only one unknown quantity, use a variable to represent it. In other words, let a variable represent what you are asked to find.

*If there are two unknown quantities and one is compared to the other, let the simplest one be represented by a variable. Then translate to represent the other quantity, using the same variable.

*If there are two unknown quantities, the total of the two is known, and there is no comparison between the two, represent one of them with a variable and the other with total minus that variable.

*If there are two or more consecutive integers, use the pattern (below) to represent them.

Read the problem again to decide if it fits into a formula or a basic setup pattern and fill in the formula or chart with the needed information.

*Geometry problems usually fit into a formula. Know the formulas for area and perimeter of a rectangle. Other formulas will be provided.

*Consecutive Integer problems, Collection problems, Mixture problems, and Distance problems usually fit into a basic setup pattern.

*Consecutive Integers set up as follows:
                        1^st = x
                        2^nd = x + 1
                        3^rd = x + 2
(If asked to find only 2 consecutive integers, leave off this one)

*Consecutive Even or Consecutive Odd Integers set up as follows:
                        1^st = x (even)                      1^st = x (odd)
                        2^nd = x + 2                          2^nd = x + 2
                        3^rd = x + 4                           3^rd = x + 4
(If asked to find only 2 consecutive integers, leave off the 3rd one)

*Collection Problems
(Amount or Quantity) times (Price) equals Money collected AP=M

Amount or Quantity 1		Amount or Quantity 2		Total Amount or Quantity
Price of item 1		Price of item 2		xxxxxxxxxxxxxxxxxxxxxxxxxx
Money collected from 1	+	Money collected from 2	=	Total Money collected

Equation:
Quantity 1 (Price 1) + Quantity 2 (Price 2) = Total Money

Total Amount or Quantity is used only if you need to represent both
Quantity 1 and Quantity 2

Do not multiply in the Totals column!
Collections: You Can't Multiply in Totals Column!

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*Mixture Problems
(Amount or Quantity) times (Price or Percent)= Price or Concentration of Mix

Equation:
Money or Concentration 1 + Money or Concentration = Price or Concentration of Mix

Total Amount or Quantity is necessary… you MUST have it…
You may add Quantity 1 and 2 to get it.

You MUST multiply the Amount/ Quantity and Price/ Percent in the Totals column!
Mixtures: You MUST multiply in the Totals Column!

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Rate 1		Rate 2
Time 1		Time 2
Distance 1 (d₁)		Distance 2 (d₂)

There are two main setups for our distance problem equations:
*d₁ + d₂ = D
The sum of the two distances equals the total distance
therefore, the total distance must be known!

*d₁ = d₂
The two distances are the same
therefore it is not necessary to know the total distance!

Use translation rules and/or charts to carefully set up
and solve the appropriate equation.

Amount or Quantity 1		Amount or Quantity 2		Total Amount or Quantity of Mix
Price or Percent 1		Price or Percent 2		Price or Percent of Total Mixture
Money or Concentration 1	+	Money or Concentration 2	=	Price or Concentration of Mix