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10 Cards in this Set
- Front
- Back
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Steps to Solve Applied Problems:
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1. Read Problem- carefully understand what is given and and what is to be found.
2. Assign a Variable- to represent the unknown value. Write down what the variable represents. If necessary express any other unknown values in terms of the variable. 3. Write an equation using the variable expression. 4. Solve the equation. 5. State the answer. Does it seem reasonable. 6. Check the answer in the words of the original problem. |
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words that translate to equal
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is, are, was, were
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Solving Problems involving sums of quanities.
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Finding two quanities when the sum of the quanities are known.choose a variable to represent one of the unknowns. then, represent the other quanity in terms of the same variable.
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Example solving problems involving sums of quanities.
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In 2004 Olympics the US won 40 more medals than China. The two countries won a total of 166 medals. How many medals did each country win?
x = China medals x + 40 = US medals 166 = total for both countries 166 = x (x + 40 ) |
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Solving problems involving three unknown quantities.
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Frequently the 3 unknowns are compared in pairs. When this happens, it is usually easiest to let the variable represent the unknown found in both pairs.
The instructions for a wood working project calls for 3 pieces of wood. The longest piece must be twice the lenght of the middle-sized piece, and the shortest piece must be 10 in shorter than the middle sized piece. Sue has a board 70 inches long to use. How long can each piece be? x = middle sized piece. 2x = longest piece x - 10 = shortest piece 70 = total board lenght x + 2x + ( x - 10 ) = 70 |
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Solve problems involving supplementary and complementary angles
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1. Two angles whos sum is 90
degrees are complementary 2. An angle that measure 90 degrees is a right angle 3. Two angles whose sum is 180 degrees are supplementary 4. If x represents the degree measure of an angle, then 90 - x = complenetary 180 - x = supplementary |
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Example solving problems involving supplementary & complementary angles
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Find the measure of an angle whose supplement is 10 degrees more than twice its complement.
x = the degree measure of an angle 90 - x = the degree measure of a complement 180 - x = The degree measure of a supplement 180 - x = 2 ( 90 - x ) + 10 |
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Solving problems involving consecutive integers
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1. Two integers that differ by one are called consecutive integers( eg. 3,4 ; 6,7; -2,-1)
2. Consecutive even integers, such as 8 and 10, differ by 2. 3. consecutive odd integers, such as 9 and 11, also differ by two. 4. In general if x = even or odd integers, then x + 2 = the next larger consecutive even or odd interger. 5. In solving consecutive integer problems if x = the first integer, then for any - two consecutive integers use x , x + 1 - two consecutive even integers use x , x + 2 - two consecutive odd integers use x , x+ 2 |
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Example problems involving consecutive integers
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Two pages that face each other in this book have 249 as sum of the page numbers. what are the page numbers.
x = lesser page x + 1 = greater page 249 = sum of page numbers x + ( x + 1 ) = 249 |
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Example problems involving consecutive odd numbers
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If the lesser of the consecutive odd integers is doubled the result is seven more than the greater of the two integers. Find the two integers.
2x = ( x + 2 ) = 7 |
