Q9. - Algebra 2

Question

Marcus tried to compute the average of his 8 test scores. He mistakenly divided the correct total S of his scores by 7. The result was 12 more than what it should have been. Which equation would determine the value of S?

$\left(A\right)8S-12=7S \left(B\right)\frac{S}{7}=\frac{S+12}{18} \left(C\right)\frac{S}{7}+12=\frac{S}{8} \left(D\right)\frac{S}{7}-12=\frac{S}{8}$

Step-by-Step Solution

Answer

The option $\left(D\right)$ is correct, the other options are incorrect, because the equation that would determine the value of $S$ is $\frac{S}{7}-12=\frac{S}{8}$.

Step 1 – Write an equation that describes the given situation.

Here S is the total score of the Marcus 8 tests.

So, the correct average score will be mathematically written as $\frac{S}{8}.$

But, mistakenly, he divided the correct total score S by 7.

This can be mathematically written as $\frac{S}{7}.$

Also, it is given that the result of $\frac{S}{7}$ is 12 more than the actual result $\frac{S}{8}.$

This means, 

$\begin{array}{c}\frac{S}{7}=\frac{S}{8}+12\\ \frac{S}{7}-12=\frac{S}{8}\end{array}$

Step 2 – Check whether the option A is correct or incorrect.

Here, in the option $\left(A\right)$ it is given that, $8S-12=7S$.

The result in step 1, one get is $\frac{S}{7}-12=\frac{S}{8}$.

So, option $\left(A\right)$ is incorrect.

Step 3 – Check whether the option B is true or false.

Here, in the option $\left(B\right)$ it is given that, $\frac{S}{7}=\frac{S+12}{18}$.

The result in step 1, one get is $\frac{S}{7}-12=\frac{S}{8}$.

So, option $\left(B\right)$ is incorrect.

Step 4 – Check whether the option C is true or false.

Here, in the option $\left(C\right)$ it is given that, $\frac{S}{7}+12=\frac{S}{8}$.

The result in step 1, one get is $\frac{S}{7}-12=\frac{S}{8}$.

So, option $\left(C\right)$ is incorrect.

Step 5 – Check whether the option D is true or false.

Here, in the option $\left(D\right)$ it is given that, $\frac{S}{7}-12=\frac{S}{8}$.

The result in step 1, one get is $\frac{S}{7}-12=\frac{S}{8}$.

So, option $\left(D\right)$ is correct.

 

Hence, the option $\left(D\right)$ is correct, the other options are incorrect, because the equation that would determine the value of S is $\frac{S}{7}-12=\frac{S}{8}$.