Problem 46 Equation 1: 3x+y = 17 Equation 2: x+3y = -1 Add equation 1 to equation 2 to get 4x+4y = 16. Divide every term by 4 to get x+y = 4. Then finally multiply both sides by 3 to get 3x+3y = 12 That shows why the answer is choice A
--------------------------------- Problem 47)
If y hours pass by, then y-(2/3)y=y/3 is the time value (2/3)y hours ago
So, Distance = rate*time d = r*t d = x*(y/3) d = (xy)/3 That's why the answer is choice B
--------------------------------- Problem 48) Let L1,L2,L3 be the three lists where L1 = {a1,a2,a3,...,ak} there are k scores here L2 = {a1,a2,...,a10} there are 10 scores here L3 = {a11,a12,...,ak} the remaining k-10 scores S(L1) = sum of the scores in list L1 M(L1) = mean of L1 = 20 = S(L1)/k M(L2) = mean of L2 = 15 = S(L2)/10 S(L1) = 20k S(L2) = 150 S(L1) = S(L2)+S(L3) M(L1) = [S(L2)+S(L3)]/k 20 = [150+S(L3)]/k 20k = 150+S(L3) S(L3) = 20k-150 M(L3) = [S(L3)]/(k-10) M(L3) = (20k-150)/(k-10) So that shows why the answer is choice E
An equation can be used to predict values from a pattern by merely substituting any value to determine the equivalent value. An example is the geometric series which has a standard equation of an = a1 * r^(n-1) and is used to predict the nth term of the series
