Mallory had an average of 87 on her first three algebra quizzes. She made the same score on the first two quizzes and 9 points higher on the third quiz. What was her grade on each quiz?

mean = sum of scores/number of scores

Let x = score on first two quizzes
87 = (2x + x+9)/3

Solve for x, then x+9.

It worked, thanks!

You are welcome.

Why did the bike go to the party alone?

Because it wanted to "score" some points with Mallory! Let's solve this algebraic mystery together, shall we?

Let's assume Mallory's grade for the first two quizzes is "X" (because who doesn't love a good mystery?). We're told she scored 9 points higher on the third quiz, so her grade for that is X + 9.

To find her average grade, we'll add up her scores and divide by the number of quizzes (which is 3).

So, her grades added up would look like this: X + X + (X + 9).

That's 3X + 9.

Dividing it by 3, we get (3X + 9) / 3 = 87.

Now, let's solve for X.

3X + 9 = 87.

Subtracting 9 from both sides gives us 3X = 78.

Dividing by 3 on both sides gives us X = 26.

Now we know Mallory's grade on the first two quizzes is 26.

For the third quiz, her grade is X + 9, which is 26 + 9 = 35.

So, Mallory scored 26 on the first two quizzes and 35 on the third quiz.

I hope that solved the mystery for you, or maybe just added a little algebraic humor to your day! Keep on solving those equations!

To find Mallory's grade on each quiz, let's work through the problem step by step.

We know that Mallory had an average of 87 on her first three algebra quizzes. Let's represent the grades on the quizzes as variables: quiz 1 as Q1, quiz 2 as Q2, and quiz 3 as Q3.

Since Mallory made the same score on the first two quizzes, we can set up the equation: (Q1 + Q2) / 2 = average

We are given that her average is 87, so we substitute that into the equation: (Q1 + Q2) / 2 = 87.

To find the grade on the third quiz, we know that it was 9 points higher than the average: Q3 = average + 9.

Now, let's solve the equation for Q1 and Q2:

(Q1 + Q2) / 2 = 87
Q1 + Q2 = 2 * 87
Q1 + Q2 = 174 -- Equation (1)

Since Mallory made the same score on the first two quizzes, we can also set up another equation: Q1 = Q2.

Now, let's substitute Q2 for Q1 in Equation (1):

Q1 + Q1 = 174
2Q1 = 174
Q1 = 87

So, Mallory's grade on the first and second quizzes is 87.

Next, let's find her grade on the third quiz using Q3 = average + 9:

Q3 = 87 + 9
Q3 = 96

Therefore, Mallory's grade on each quiz is 87, 87, and 96 for the first, second, and third quizzes, respectively.