SOLUTION: Allanʹs 4 quiz scores in his math class are 87, 89, 88, and 78. What score does he need to obtain on his exam to average an 85 if an exam counts as much as two quizzes?

Question 1196293: Allanʹs 4 quiz scores in his math class are 87, 89, 88, and 78. What score does he need to obtain on
his exam to average an 85 if an exam counts as much as two quizzes?
Found 5 solutions by josgarithmetic, math_tutor2020, MathLover1, amoresroy, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
v, the score for each of the two next 'quizzes'.
2v, the score for this "exam".

The count of quizes already done is 4.
The exam will add two more quizzes.

Solve.
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = score on the exam
2x = equivalent score on a quiz (since the exam counts for two quizzes)
For instance if you got an 82 on the exam, then it is equivalent to 2*82 = 164 points for a quiz.
It might be helpful to think of it like getting 82's on two different extra quizzes.

It also might be helpful to think of the 2x as x+x
So that we can break things further down

A = set of scores
A = {87, 89, 88, 78, x, x}
Note I listed x twice
There are 6 elements in set A

Now compute the average. Do so by adding up the scores and dividing by the number of scores (6)
So we get:
(87+89+88+78+x+x)/6
which simplifies to
(342+2x)/6

Set this average equal to the target 85 and solve for x.
(342+2x)/6 = 85
342+2x = 6*85
342+2x = 510
2x = 510-342
2x = 168
x = 168/2
x = 84

Answer: 84

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
let quiz score be
if an exam counts as much as two quizzes, then exam score will be
the total number of scores will be same as 6 quizzes
if average should be , then we have

score he need to obtain on his exam to average an is
check:
-> true

Answer by amoresroy(361)   (Show Source): You can put this solution on YOUR website!
Let x = the score Allan needs to obtain in his exam
Given that the exam counts as much as two quizzes, the total average of 85 is calculated as follows:
(87 + 88 + 89 + 78 + 2x)/6 = 85*6
342 + 2x = 510
2x = 510 - 342
x = 168/2
x = 84
Answer:
Allan needs to obtain a score 84 in his exam to get average of 85.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

You have 4 responses already; however, they are all very similar, so I will show a different method that is sometimes convenient to use in a problem involving the average of several numbers that are relatively close together.

Comparing each quiz score to the desired average, we have the following:
87: +2 89: +4 88: +3 78: -7 ------- total: +2

All together, the 4 quiz scores are +2 compared to the desired average. Since the test counts as much as 2 quizzes, the score on the test, to balance the scores on the quizzes, must be -1 compared to the desired average. So the score on the test to make an average of 85 is 85-1 = 84.

ANSWER: 84

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