Start with concise, clear, complete definitions -- Always!
"Aura took three biology exams and has an average score of 88.her second exam score was 10 points better than her first. And her 3rd exam score was better then her 2nd exam. What were her three exam scores?"
I'm not sure we have the whole problem statement, but I'll just plough ahead and see what happens.
E = Exam Score #1
F = Exam Score #2
G = Exam Score #3
That's all it takes. Then we can read the problem statement.
"Aura took three biology exams and has an average score of 88"
(E+F+G)/3 = 88
"her second exam score was 10 points better than her first"
F = E + 10 or E = F - 10
"her 3rd exam score was better then her 2nd exam [score]"
G > F
Start from the top.
(E+F+G)/3 = 88
Multiply by 3
E+F+G = 264
Substitute E = F - 10
(F-10)+F+G = 264
Simplify
2F + G = 274
Here's where we have a bit of a problem. G > F doesn't quite give us an obvious substitution. Let's just play around a bit and see what we can make it do. It's only an equation or two. We won't break it.
SUPPOSE G = F+1, then 3F + 1 = 274 ==> F = 91 and G = 92 and E = 81
Check: (81+91+92)/3 = 264/3 = 88
SUPPOSE G = F+2, then 3F + 2 = 274 ==> F = 90.666 and G = 92.666 and E = 80.666
Check: (80.666+90.666+92.666)/3 = 264/3 = 88
This gives us a bit of a problem. Do we have fractional scores or are they all integers? The problem is silent on this point. Let's just keep going, but only look at the integer solutions.
SUPPOSE G = F+3, then 3F + 3 = 274 ==> F = 90.333 and G = 93.333 and E = 80.333
Check: (80.333+90.333+93.333)/3 = 264/3 = 88
SUPPOSE G = F+4, then 3F + 4 = 274 ==> F = 90 and G = 94 and E = 80
Check: (80+90+94)/3 = 264/3 = 88
SUPPOSE G = F+7, then 3F + 7 = 274 ==> F = 89 and G = 96 and E = 79
Check: (79+89+96)/3 = 264/3 = 88
SUPPOSE G = F+10, then 3F + 10 = 274 ==> F = 88 and G = 98 and E = 78
Check: (78+88+98)/3 = 264/3 = 88
SUPPOSE G = F+13, then 3F + 13 = 274 ==> F = 87 and G = 100 and E = 77
Check: (77+87+100)/3 = 264/3 = 88
And G
can't be 14 greater than F, unless there is an extra credit provision.
Nothing like a good problem statement to help us avoid unnecessary work. If you had told us from the beginning the Score #3 was four(4) greater than Score #2, this would have been much simpler.
