Hope this helps. Let me know if you have more questions.
You need to understand that you're solving for the average, which you already know: 90. Since you know the values of the first three exams, and you know what your final value needs to be, just set up the problem like you would any time you're averaging something.
Solving for the average is simple:
Add up all of the exam scores and divide that number by the number of exams you took.
(87 + 88 + 92) / 3 = your average if you didn't count that fourth exam.
Since you know you have that fourth exam, just substitute it into the total value as an unknown, X:
(87 + 88 + 92 + X) / 4 = 90
Now you need to solve for X, the unknown:
87
+
88
+
92
+
X
4
(4) = 90 (4)
Multiplying for four on each side cancels out the fraction.
So now you have:
87 + 88 + 92 + X = 360
This can be simplified as:
267 + X = 360
Negating the 267 on each side will isolate the X value, and give you your final answer:
X = 93
Now that you have an answer, ask yourself, "does it make sense?"
I say that it does, because there were two tests that were below average, and one that was just slightly above average. So, it makes sense that you'd want to have a higher-ish test score on the fourth exam.
Given:
(4k⁷)³ = 4n(k⁷)³
Note that (aˣ)ⁿ = aˣⁿ
Expand the left and right sides.
4³k²¹ = 4nk²¹
Divide each side by k²¹.
4³ = 4n
Divide each side by 4.
4² = n
Therefore
n = 4² = 16
Answer: n = 16
$123 = ($3b + $8.50c)
b + c = 30
b = 24 birds ($72)
c = 6 cats ($51)
51+72=123
There were 24 birds at the shelter on Tuesday.
