SAMPLE College Math
Writtensentencescanbeconvertedintomathematicalexpressionssothattheycanbesolvedtoarrive at meaningful solutions. For instance, “a number is multiplied by 10 and then added to 8toget48”. Assume the number is and the mathematical equation becomes: 10 + 8 = 48 It shouldbenotedthatthetwosidesoftheequationshouldbalanceeachotherusingtheequalto(=) sign. Let us solve a few more examples to get a better understanding.
Word Problem
Algebraic Translation
( 2 2+ 1 0 ) = 35 2 – 6 – 5 = 3
Kathyaskshermotherhowoldsheis.Hermotherreplies,“Ifyou double my age and add 10 to it, then divide by 2, you get 35.”
Marlingetshismonthlypocketmoney.Hesaveshalfofit,andthen makes two purchases worth $6 and $5. Finally whenhereaches home, he is left with $3.
A bus starts leaves the station filledtocapacity.Atthefirststop, halfthepassengersgetoffand10getonboard.Atthenextstation, 12getoffwhile15getonboard.Now,thenumberofpassengersin the bus is 28.
− 2 + 10 − 12 + 15 = 28
D. Mathematical Translations of Inequalities from Words Inequalities can also be translated from wordsintomathematicalequations.Forinstance,weneedto translate the sentence, “a number minus 6 is less than 2” into an inequality. “A number” states the presence of an unknown variable. Let us denote that by . Aftersubtracting6from ,thisexpression should be less than (denoted by inequality sign <) 2. Now the expression becomes: –6 < 2 Similarly, mathematical expressions can be formed using differentinequalitynotationslikemorethan (>), less than (<), at most (≤), at least (≥), etc., as shown below.
+ 5 < 15 5 ≤25 − 5≥17 > 65
The sum of 5 more than the number is no more than 15
Five boxes of cereal costs at most 25 dollars
The difference between a number and 5 is at least 17
Jenny’s height is greater than 65 inches
E. Solving Equations Inordertosolvetheequations,itisimportanttomoveallvariablestoonesideusinginverseoperations (addition subtraction & multiplication division). It should be noted that applying inverse operations on both sides ofanequationkeepsthebalance.Forinstance,theequation canbe –3 = 7
© 2023 ACHIEVE ULTIMATE CREDIT-BY-EXAM GUIDE|COLLEGE MATH
5
Made with FlippingBook - Online Brochure Maker