How to I Calculate the Missing Values?

#1
IQ-scores are standard-score transformed scores having a mean of 100 and a standard deviation of 15; SAT scores are standard-score transformed scores having a mean of 500 and a standard deviation of 100. In what follows, X refers to a raw score from a distribution with a mean of X and a standard deviation of S, and SAT and IQ refer to the corresponding transform of that score. Solve for the missing value in each of the following:
(a) X = -3; X= -9; S = ?; IQ = 130
(b) X = -.5; X=? ; S = .5; SAT = 800
(c) X = ?; X= 50; S = 12; IQ = 85
(d) X = 60; X= 62; S= ?; SAT = 450
(e) X = 52; X= 40; S = 6; IQ= ?

I tried using the z-score formula and solving for the missing values, but the numbers I got were defiantly not right. Is there a different way to solve them or did I just mess up doing it the first time?
 
#2
All of these numbers are set up to be very simple calculations. You need to understand the concept of standard deviation and standardized scores. Let me take question (e) for example, to get you started. The raw score is 52, the mean is 40, and the standard deviation is 6. Conveniently, the raw score is exactly two standard deviations higher than the mean. Now if we want to standardize this score given what we are told about standard IQ scores, the correct answer would be two standardized standard deviations above the standardized mean (15 and 100).

Can you figure them out based on this? You can probably do most of this in your head without any complex calculations.
 
#4
The raw score is 52, the mean is 40, the standard deviation is 6.

52 is 12 more than 40

12 is two standard deviations (2*6=12)

for IQ mean is 100 and sd is 15

2 standard deviations above 100 is 130