Question 100427This question is from textbook
: Juanita's spelling average was between 80 and 90. if she scored eight points more on the second test than on the first test and 5 points less on the third test than on the first test. what scores are possible for the first test
This question is from textbook
Answer by joyofmath(189)   (Show Source):
You can put this solution on YOUR website! Let t1, t2, and t3 be the scores on tests 1, 2, and 3.
If Juanita's average was between 80 and 90 then her TOTAL for the three tests was between 240 and 270.
So, 240 <= t1+t2+t3 <= 270
J scored 8 points higher on the 2nd test than the 1st, so t2=t1+8
J scored 5 points less on the 3rd test than the 1st, so t3=t1-5
So, 240 <= t1+(t1+8)+(t1-5) <= 270
Or, 240 <= 3*t1+8-5 <= 270
Or, 240 <= 3*t1+3 <= 270
Or, 240 <= 3*(t1+1) <= 270
Or, 80 <= t1+1 <= 90
Or, 79 <= t1 <= 89
So, J scored between 79 and 89 on the 1st test.
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