Problema Solution
A psychologist found that the relationship between scores on two tests, test A and test B, was perfectly linear. Joe scored 32 on test A and 70 on test B; Sue scored 45 on test A and 96 on test B. If Jake scored 40 on test A, what would he score on test B? If Charles scored 80 on test B, what would he score on test A?
Answer provided by our tutors
let
a = the scores on test A
b = the scores on test B
the relationship between scores on two tests, test A and test B, was perfectly linear means:
a = s*b + t, where s and t are constants
Joe scored 32 on test A and 70 on test B means a = 32, b = 70
32 = 70s + t
70s + t = 32
Sue scored 45 on test A and 96 on test B means a = 45 and b = 96
45 = 96s + t
96s + t = 45
by solving the system of equations:
70s + t = 32
96s + t = 45
we find
s = 0.5
t = -3
click here to see the step by step solution of the system of equations:
the linear equation that describes the relationship between scores on two test is:
a = 0.5b - 3
If Jake scored 40 on test A, what would he score on test B?
a = 40, we need to find b
40 = 0.5b - 3
by solving we find
b = 86
click here to see the step by step solution of the equation
Jake scored 86 on the test B.
If Charles scored 80 on test B, what would he score on test A?
b = 80 and we need to find a
a = 0.5*80 - 3
by solving we find
a = 37
click here to see the step by step solution of the equation
Charles scored 37 on the test A.