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jeffhn90
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four steps
 1. id what value the question is asking for (desired value)
 2. id unknown values and label them with variables
 3. id relationships and translate them into equations
 4. use the equation to solve for the desired value

additive relationships  subj. algebraic translation
 adding terms with the same units does not change the units
 the units of every term are the same

multiplicative relationships  subj. algebraic translation
 treat units like numerators and denominators
 units that are multiplied together DO change

common relationships  subj. algebraic translation
 total cost ($) = unit price ($/unit) x quantity purchased (units)
 profit ($) = revenue ($)  cost ($)
 total earnings ($) = wage rate ($/hour) x hours worked (hours)
 miles = miles per hour x hours
 miles = miles per gallons x gallons


Integer Constraints
ex. If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates? (54, 55, 56, 57, 58)
If Kelly received 1/3 more votes than Mike, she received 4/3 the number of votes. So what times 4/3 will equal an integer? only multiple of 3 will cancel out the 3 in the denominator. the number of votes Mike received is a multiple of 3, then the number of votes Kelly received must be a multiple of 4. Taken together, the total number of votes cast must then be a multiple of 7. (answer is 56)

Hidden Constraint
DS ex. A store sells erasers for $0.23 each and pencils for $0.11 each. How many erasers and pencils did Jessica buy from the store?
(1) Jessica bought 5 erasers
(2) Jessica spent $1.70 on erasers and pencils
 Statement 1 by itself is not sufficient
 On the surface, statement 2 should not be enough.
 If J bought 1 eraser, 170  23 = 147 cents on pencils (but 147 isn't divisible by 11)
 ... If J bought 5 erasers and 5 pencils: 5(23) + 5(11) = 170
 thus, statement 2 is sufficient by itself

