Hi All,
This question is perfect for TESTing THE ANSWERS (we're looking for an answer that divides evenly into 336 AND - when you add 6 to it - evenly divides into 462. How long would it take you to do the necessary division to find that answer?). The "math" approach to this prompt can actually be done in a number of ways, depending on how you want to set up the algebra. Here's another way:
Since a "tankful" of gasoline is the same number of gallons of gas whether driving on the highway or driving in the city, we can use a variation of the Distance Formula to create 2 equations:
462 = H(G) where H = miles/gallon on the highway and G = # of gallons
336 = C(G) where C = miles/gallon in the city and G = # of gallons
Right now, we have 3 variables and 2 equations. The last sentence gives us one more equation to work with: "the car traveled 6 fewer miles per gallon in the city than on the highway." This translates into:
C = H - 6
So now we have a "system" of equations (3 variables and 3 unique equations means that we CAN solve for all 3 variables). We're trying to solve for C…..
462 = H(G)
336 = C(G)
C = H - 6
H = C + 6 plug this into the first equation….
462 = (C+6)(G)
462 = CG + 6G
336 = CG plug this into the prior equation….
462 = 336 + 6G
126 = 6G
21 = G
**REMINDER: This is the value of G. We want the value of C.**
Plug G=21 into 336 = CG
336 = C(21)
16 = C
Final Answer:
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