SOLUTION: In maths exam the marks range from 24 to 84. The original marks are to be scaled so that lowest new mark is 30 and the highest new mark is 120 The formula is to be of type y =ax+b

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Question 144411: In maths exam the marks range from 24 to 84. The original marks are to be scaled so that lowest new mark is 30 and the highest new mark is 120
The formula is to be of type y =ax+b where x is the original mark and y is the new mark
Write down two simultaneous equations for a and b. hence find the required formula
Answer by ankor@dixie-net.com(22740) (Show Source):
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In maths exam the marks range from 24 to 84. The original marks are to be scaled so that lowest new mark is 30 and the highest new mark is 120
The formula is to be of type y = ax+b where x is the original mark and y is the new mark
Write down two simultaneous equations for a and b. hence find the required formula
:
Assign the values: x1 = 24, y1 = 30
Using the formula y = ax + b
30 = 24a + b
or
24a + b = 30
and
Assign the values: x2 = 84; y2 = 120
84a + b = 120
:
take these two equations
84a + b = 120
24a + b = 30
---------------subtracting eliminates b, find a
60a + 0 = 90
a =
a = 1.5
;
Find b using 24a + b = 30
24(1.5) + b = 30
36 + b = 30
b = 30 - 36
b = -6
:
The equation for this problem: y = 1.5x - 6