An equation or a statement of equality is a relationship between quantities. In word problems, you will be looking for relationships or connections. In simpler, more direct cases, the verb of the sentence can be translated into an equal sign. The verb in each example below is highlighted. Notice that it translates in each case to an equal sign. EXAMPLES |
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34 is what percent of 17? Let x = the percent (in decimal form) 34 is what percent of 17
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Three more than twice a number yields ten more than the number. Let x = the number Three
more than twice a number
yields
ten
more than the
number. 2x + 3 = x + 10 x = 7 |
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A sweater is on sale for $12. This represents a 20% mark down from the original. What original price of the sweater? Sale Price = Regular Price - Markdown It
would be helpful to paraphrase. The red words represent the same thing: $12
represents
a 20% mark down from the
original. What is the original price of the sweater? Sale Price = Regular Price - Markdown 12 = x - 0.20x 12 = 0.80x x = 15 The original price of the sweater was $15.
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Sometimes the relationship is not directly stated. You will need to look for indirect relationships or connections. It is helpful to paraphrase the word problem in a more direct fashion in order to see the relationships clearly. Look for formulas, use common sense, read carefully and don't give up. EXAMPLES |
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The town's water department charges $7 per month, plus 42 cents for every 100 gallons of water used. Last month, one homeowner received a bill for $17.98. How many gallons of water was the homeowner charged for using? Analysis
Solution |
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17.98 = 7 + 0.0042W |
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17.98 = 7
+ 0.0042W |
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The homeowner used 2,614 gallons of water. | ||
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Three hundred employees were absent from work one day. This was twenty percent of the the total number of people employed by the company. How many people does the company employ? Analysis
Solution |
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Translate to an equation |
300 equals
0.20 times X 300 = 0.20X |
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Solve the equation |
300 = 0.20X 0.20 0.20 1500 = X |
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Answer the question |
The company employs 1500 people. | ||
Introduction Translation Guide Writing Equations Multiple Unknowns General Problem-solving Guide
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