# algebraic equation problem

May 28th, 2015
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Example 1. ax ± b = c. All problems like the following lead eventually to an equation in that simple form.Jane spent \$42 for shoes. This was \$14 less than twice what she spent for a blouse. How much was the blouse?

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Example 1. axb=c.All problems like the following lead eventually to an equation in that simple form.Jane spent \$42 for shoes. This was \$14 less than twice what she spent for a blouse. How much was the blouse?Solution.Every word problem has anunknownnumber. In this problem, it is the price of the blouse. Always letxrepresent the unknown number. That is, letxanswer the question.Letx, then, be how much she spent for the blouse. The problem states that "This" -- that is, \$42 -- was \$14 lessthan two timesx.Here is the equation: 2x 14=42.2x=42 + 14 (Lesson 9)=56.x=562=28.The blouse cost \$28.Example 2.There arebboys in the class. This is three more than four times the number of girls. How many girls are in the class?Solution. Again, letxrepresent the unknown number that you are asked to find: Letxbe the number of girls.(Althoughbis not known, it is not what you are asked to find.)The problem states that "This" --b-- is three more than four timesx: 4x+ 3=b.Therefore,4x=b 3x=b 34.The solution here is not a number, because it will depend on the value ofb. This is a type of "literal" equation, which is very common in algebra.Example 3. The whole is equal to the sum of the parts.The sum of two numbers is 84, and one of them is 12

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