Question

Eduardo has taken four 100-point tests. With each test, his score improved by 2 points. If he earned a total of 356 points across the four tests, what did he score on the fourth test?

Answer 1

Let the score on the first test be \( x \). According to the problem, Eduardo's scores on the four tests can be represented as:

1. First test: \( x \)
2. Second test: \( x + 2 \)
3. Third test: \( x + 4 \)
4. Fourth test: \( x + 6 \)

We know from the problem that the total score across all four tests is 356 points. We can set up the following equation based on Eduardo's scores:

\[
x + (x + 2) + (x + 4) + (x + 6) = 356
\]

Simplifying the left side, we combine the terms:

\[
x + x + 2 + x + 4 + x + 6 = 356
\]
\[
4x + 12 = 356
\]

Next, we isolate \( 4x \) by subtracting 12 from both sides:

\[
4x = 356 - 12
\]
\[
4x = 344
\]

Now, we divide both sides by 4 to solve for \( x \):

\[
x = \frac{344}{4} = 86
\]

Thus, the scores for the four tests are:

1. First test: \( x = 86 \)
2. Second test: \( x + 2 = 86 + 2 = 88 \)
3. Third test: \( x + 4 = 86 + 4 = 90 \)
4. Fourth test: \( x + 6 = 86 + 6 = 92 \)

We are interested in the score of the fourth test, which is

\[
\boxed{92}
\]

To verify, we can check if the total of the scores equals 356:

\[
86 + 88 + 90 + 92 = 356
\]

Calculating:

\[
86 + 88 = 174
\]
\[
174 + 90 = 264
\]
\[
264 + 92 = 356
\]

Since the total after checking is correct, the score on the fourth test is indeed

\[
\boxed{92}
\]