Question

Angela’s average for six math tests is 87. On her first four tests she had scores of 93, 87, 82, and 86. On her last test, she scored 4 points lower than she did on her fifth test. What scores did Angela receive on her fifth and sixth tests?


fifth test = 85; sixth test = 89


fifth test = 89; sixth test = 85


fifth test = 85; sixth test = 81


fifth test = 90; sixth test = 86

Answer 1

To find the scores Angela received on her fifth and sixth tests, we will use the information given about her average score, which is 87 over six tests.

1. **Calculate the total score for six tests**:
\[
\text{Total score for six tests} = \text{Average} \times \text{Number of tests} = 87 \times 6 = 522
\]

2. **Calculate the total score from the first four tests**:
The scores for the first four tests are 93, 87, 82, and 86. We find the sum of these scores:
\[
93 + 87 + 82 + 86 = 348
\]

3. **Determine the total score needed from the fifth and sixth tests**:
To find the scores for the fifth and sixth tests, we subtract the sum of the first four tests from the total score:
\[
\text{Score for fifth and sixth tests} = 522 - 348 = 174
\]

4. **Define the fifth test score**:
Let the score on her fifth test be \( x \). The score on her sixth test is \( x - 4 \) since she scored 4 points lower on the sixth test.

5. **Set up the equation**:
We have:
\[
x + (x - 4) = 174
\]
Simplifying:
\[
2x - 4 = 174
\]
\[
2x = 178
\]
\[
x = 89
\]

6. **Calculate the sixth test score**:
\[
\text{Sixth test} = 89 - 4 = 85
\]

Thus, Angela received a score of 89 on her fifth test and 85 on her sixth test.

The final answer is:
**fifth test = 89; sixth test = 85**.