Cracking The SAT Premium

32. 4 When dealing with values that are directly proportional, you can use the equation .

For this    question,   you can call    the number  of  hours   spent   playing Call    of  Destiny x   and the

number  of  hours   spent   in  the game    room    y.  Your    equation    will    then    look    like    this:   .

Cross-multiply  to  get 6y 2    =   3(8)    or  6y 2    =   24. Divide  both    sides   of  the equation    by  6   to  get

y 2     =   4.

33. 
    

    13.5 Start by translating English to math. Make s the price of Smooth-Glide pens and e the price
    of Easy-Write pencils. If 12 pens and 8 pencils cost $16, then 12s + 8e = 16. Similarly, if 6
    pens and 10 pencils cost $11, then 6s + 10e = 11. Remember to Read the Full Question! The
    question wants the price of 9 pens and 9 pencils. If you stack the equations and add, you get
    18 s + 18e = 27. This is exactly double the number of pens and pencils you want, so divide
    the entire equation by 2 to get 9s + 9e = 13.5.

    
    


34. 
    

    2 or

    
    

There   are a   few different   ways    to  approach    this    question.   Since   the calculator  is  permitted

on  this    section of  the test,   you can put the equation    into    the standard    ax^2    +   bx  +   c   =   0   form

and plug    that    equation    into    the “y  =”  button  on  your    graphing    calculator. The equation,   once

rearranged, is  3x^2    –   16x +   20  =   0.  You can trace   the graph   or  use the “calc”  feature to

calculate   the zeroes, which   are the same    as  the values  of  x.  Doing   so  will    yield   values  of  x

=    2   and    x    =   3.33.   Alternatively,  you     can     factor  the     equation    the     long    way     or  use     the

quadratic   formula,     .  In  this    equation,   a   =   3,  b   =   –16,    and c   =   20. Plugging

those    values  into    the     equation,   you     get    

. Therefore, the solutions are

    and     =   2.  Either  value   (   or  2)  is  a   valid   answer.

35. 5 Since you are looking for the value of x for which the population surpassed the number of
    dwellings, you can set up an inequality: 3x > 2x + 100. Now, simply plug in values for x
    starting with x = 1 until the left-hand side of the inequality is larger than the right-hand side.
    Using the values x = 1, x = 2, x = 3, and x = 4, you will find that the left-hand side of the
    inequality is less than the right-hand side. Using x = 5, 3^5 = 243, and 2(5) + 100 = 110,