Question 100427
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.