Question

On an Algebra test, the number of students who got an A was three more than twice the number of students who got lower grades. How many A's were there if the total number of students in the Algebra class is 24?

Answer 1

Let \( x \) represent the number of students who got lower grades. According to the problem statement, the number of students who got an A can be expressed as:

\[
2x + 3
\]

We also know that the total number of students in the Algebra class is 24. Therefore, we can set up the equation:

\[
x + (2x + 3) = 24
\]

Now, simplify the left side of the equation:

\[
x + 2x + 3 = 24
\]

Combine like terms:

\[
3x + 3 = 24
\]

Next, subtract 3 from both sides to isolate the term with \( x \):

\[
3x = 24 - 3
\]

This simplifies to:

\[
3x = 21
\]

Now, divide both sides by 3 to solve for \( x \):

\[
x = 7
\]

This means there were 7 students who got lower grades. Now, we can find the number of students who got an A:

\[
2x + 3 = 2(7) + 3 = 14 + 3 = 17
\]

Thus, the number of students who received an A is

\[
\boxed{17}
\]

To confirm, we can check the total number of students:

- Students with lower grades: \( x = 7 \)
- Students with A's: \( 17 \)

Adding these gives:

\[
7 + 17 = 24
\]

This matches the total number of students in the class, confirming our solution is correct. The number of A's is indeed \( \boxed{17} \).