SOLUTION: 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,

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Question 206266: 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
Found 2 solutions by nerdybill, Edwin McCravy:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!

Answer is E:
5g+50
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
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
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