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Translating Word Problems: Examples (page 2 of 2)

Sections: Keywords, Worked examples

• Translate "the sum of 8 and y" into an algebraic expression.

This translates to "8 + y"

• Translate "4 less than x" into an algebraic expression.

This translates to "x – 4"

• Translate "x multiplied by 13" into an algebraic expression.

This translates to "13x"

• Translate "the quotient of x and 3" into an algebraic expression.

This translates to " ^x/₃"

• Translate "the difference of 5 and y" into an algebraic expression.

This translates to "5 – y"

• Translate "the ratio of 9 more than x to x" into an algebraic expression.

This translates to "(x + 9)/x"

• Translate "nine less than the total of a number and two" into an algebraic expression, and simplify.

This translates to "(n + 2) – 9", which then simplifies to "n – 7"

Here are some more wordy examples:

• The length of a football field is 30 yards more than its width. Express the length of the field in terms of its width w.

Whatever the width w is, the length is 30 more than this. Recall that "more than" means "plus that much", so you'll be adding 30 to w.

The expression they're looking for is "w + 30".

This one is important: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

• Twenty gallons of crude oil were poured into two containers of different size. Express the amount of crude oil poured into the smaller container in terms of the amount g poured into the larger container.

The expression they're looking for is found by this reasoning: There are twenty gallons total, and we've already poured g gallons of it. That means that there are 20 – g gallons left.They want the answer "20 – g".

This is the "how much is left" construction. That is, you have two amounts that add up to some total, but all you are given is the value of the total. Then the two amounts are the first amount, and however much is left, with the second amount being this amount that is left. I'm making a big deal about this "how much is left" construction because it comes up a lot and tends to cause a lot of confusion. Make sure you understand this one!

Once you've learned to translate phrases into expressions and sentences into equations, you are ready to dive into word problems. Of course, there are jillions of word problems (physics is all word problems; business math is all word problems; your whole life is an essay question...c'mon, smile!), but there are some basic types of word problems that you can expect to see in your algebra class. I've done a few examples:

"Age" problems, involving figuring out how old people are (or will be)
"Area/volume/perimeter" problems, involving very basic geometric formulas
"Coin" problems, involving figuring out how many of each type of coin you have
"Distance" problems, involving speed/rate, distance, time, and the formula "d = rt".
"Investment" problems, involving investments, interest rates, and the formula "I = Prt".
"Mixture" problems, involving combining elements and find prices (of the mixure) or percentages (of, say, acid or salt).
"Number" problems, involving "Three more than two times the smaller number..."
"Percent of" problems, involving finding percents, increase/decrease, discounts, etc.
Quadratic word problems, such as projectile motion and max/min questions.
"Work" problems, involving two or more people or things working together to complete a task, and finding how long they took.

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