Question

tony has scored 75, 65, 77, 62, and 87 on his previous five tests. what score does he need on his next test so that his average (mean) is 74?

Explanation:

Step1: Recall the mean formula

The mean formula is $\text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}$. Let the score on the next test be $x$. The sum of the scores of the six tests is $75 + 65+77 + 62+87+x$, and the number of tests is 6. We know the mean should be 74.

Step2: Set up the equation

$74=\frac{75 + 65+77 + 62+87+x}{6}$. First, find the sum of the first - five scores: $75+65 + 77+62+87=366$. So the equation becomes $74=\frac{366 + x}{6}$.

Step3: Solve the equation for $x$

Multiply both sides of the equation by 6: $74\times6=366 + x$. Since $74\times6 = 444$, we have $444=366+x$. Then subtract 366 from both sides: $x=444 - 366$.

Answer:

78