An old grading system describes grades from 0 to 10. New grading guidelines require that grades be entered from 50 to 100. Which expression can be used to convert an old grade, g, to the new grade?
A) 5g
B) g+50
C) g+90
D) 10g-50
E) 5g+50
Such an expression would have to convert g=0 to 50, and g=10 to 100.
Let's try each of those answers and see which, if any, of them
do that.
Let's try:
A) 5g
Let's see if 5g converts g=0 to 50:
Substituting 0 in 5g gives 5(0) or 0. No that doesn't convert
g=0 to 50. It converts it back to 0. So there is no use trying
to see if it converts g=10 to 100. (It doesn't, btw)
So we have ruled out choice A)
Let's try out
B) g+50
Let's see if g+50 converts g=0 to 50:
Substituting 0 in g+50 gives 0+0 or 50. YES, that does convert
g=0 to 50. However it also must convert g=10 to 100.
Let's see if g+50 converts g=10 to 100:
Substituting 10 in g+50 gives 10+50 or 60. NO, that does convert
g=10 to 100. It converts it to 60.
So we have ruled out choice A)
Let's try out:
C) g+90
Let's see if g+90 converts g=0 to 50:
Substituting 0 in g+90 gives 0+90 or 90. No that doesn't convert
g=0 to 50. It converts it to 90. So there is no use trying
to see if it converts g=10 to 100. (It DOES, btw! but it doesn't
convert 0 to 50)
So we have ruled out choice C)
Let's try out:
D) 10g-50
Let's see if 10g-50 converts g=0 to 50:
Substituting 0 in 10g-50 gives 10(0)-50 or -50. No that doesn't convert
g=0 to 50. It converts it to -50. So there is no use trying
to see if it converts g=10 to 100. (It DOES, btw! but it doesn't
convert 0 to 50)
So we have ruled out choice D)
Let's try out:
E) 5g+50
Let's see if 5g+50 converts g=0 to 50:
Substituting 0 in 5g+50 gives 5(0)+50 or 50. YES that does convert
g=0 to 50. However it also must convert g=10 to 100.
Let's see if 5g+50 converts g=10 to 100:
Substituting 10 in 5g+50 gives 5(10)+50 or 100. YES, that does convert
g=10 to 100.
So the correct choice is E)
Edwin
