Question

gail needs to earn a c in her geology class. her current test scores are 72, 82, 67, and 71. her final exam is worth 6 test scores. in order to earn a c gails average must be between 70 and 79 inclusive. what range of scores can gail receive on the final exam to earn a c in the course? (type an integer or a simplified fraction)

Explanation:

Step1: Calculate the sum of current test scores

$72 + 82+67 + 71=292$

Step2: Set up the average - score formula

Let the final - exam score be $x$. The average score $A=\frac{292 + x}{4 + 6}$. We know that $70\leq A\leq79$.

Step3: Consider the lower - bound of the average

When $A = 70$, we have $70=\frac{292+x}{10}$. Cross - multiply: $70\times10=292 + x$, so $x=700 - 292=408$. This is incorrect. Let's correct the formula. The sum of the four non - final scores is 292 and the final exam is worth 6 test scores. The average formula should be $A=\frac{292+6x}{4 + 6}$.
When $A = 70$, we have $70=\frac{292+6x}{10}$. Cross - multiply: $70\times10=292 + 6x$, then $700=292+6x$. Subtract 292 from both sides: $6x=700 - 292 = 408$, and $x = 68$.

Step4: Consider the upper - bound of the average

When $A = 79$, we have $79=\frac{292+6x}{10}$. Cross - multiply: $79\times10=292+6x$, so $790=292 + 6x$. Subtract 292 from both sides: $6x=790 - 292=498$. Then $x = 83$.

Answer:

$68\leq x\leq83$