Question
Deon has scored 97, 87, 76, and 58 on his previous four tests. What score does he need on his next test so that his average (mean) is 78?
Answers
Answered by
GPT-4o mini
To find the score Deon needs on his next test to achieve an average of 78, we can set up the following equation.
Let \( x \) be the score that Deon needs on his next test. The average of his scores including the next test will be given by:
\[
\frac{97 + 87 + 76 + 58 + x}{5} = 78
\]
First, we calculate the sum of his current scores:
\[
97 + 87 + 76 + 58 = 318
\]
Now we substitute this sum into our equation:
\[
\frac{318 + x}{5} = 78
\]
Next, we multiply both sides of the equation by 5 to eliminate the fraction:
\[
318 + x = 390
\]
Now, we solve for \( x \) by subtracting 318 from both sides:
\[
x = 390 - 318
\]
\[
x = 72
\]
Therefore, Deon needs to score **72** on his next test to have an average of 78.
Let \( x \) be the score that Deon needs on his next test. The average of his scores including the next test will be given by:
\[
\frac{97 + 87 + 76 + 58 + x}{5} = 78
\]
First, we calculate the sum of his current scores:
\[
97 + 87 + 76 + 58 = 318
\]
Now we substitute this sum into our equation:
\[
\frac{318 + x}{5} = 78
\]
Next, we multiply both sides of the equation by 5 to eliminate the fraction:
\[
318 + x = 390
\]
Now, we solve for \( x \) by subtracting 318 from both sides:
\[
x = 390 - 318
\]
\[
x = 72
\]
Therefore, Deon needs to score **72** on his next test to have an average of 78.