on three examinations, dana received scores of 82, 93, and 72. what score does dana need on the fourth…

on three examinations, dana received scores of 82, 93, and 72. what score does dana need on the fourth examination to raise his average to 85?

on three examinations, dana received scores of 82, 93, and 72. what score does dana need on the fourth examination to raise his average to 85?

Answer

Explanation:

Step1: Recall the average formula

The average of $n$ numbers $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{x_1 + x_2+\cdots+x_n}{n}$. Here $n = 4$, and we know $x_1=82$, $x_2 = 93$, $x_3=72$, and we want $\bar{x}=85$. Let the fourth - score be $x$. Then $85=\frac{82 + 93+72+x}{4}$.

Step2: Cross - multiply

Multiply both sides of the equation $85=\frac{82 + 93+72+x}{4}$ by 4. We get $85\times4=82 + 93+72+x$.

Step3: Calculate the right - hand side sum

First, calculate $82 + 93+72=247$. So the equation becomes $340=247+x$.

Step4: Solve for $x$

Subtract 247 from both sides of the equation $340=247+x$. We have $x=340 - 247=93$.

Answer:

93