Q32. - Algebra 2

Question

For exercises 31 and 32, define a variable, write an equation or inequality, and solve the problem.

32. To receive a B in his English class, Nick must have an average score of at least 80 on five tests. He scored 87,89,76 and 77 on his first four tests. What must he score on the last test to receive a B in the class?

Step-by-Step Solution

Answer

Nick must score at least 71 in the last test to receive a B in the class.

Step 1 – Description of step.

To receive a B in his English class, minimum score needed in the five tests is 80. Nick scored 87,89,76 and 77 on his first four tests.

 

Let x be the score required in fifth test to receive B in the class.

Step 2 – Description of step.

Write an equation or inequality using the given information.

 

$\frac{x+87+89+76+77}{5}\ge 80$

Step 3 – Description of step.

Add all the numbers in the numerator.

 

$\frac{x+329}{5}\ge 80$

Step 4 – Description of step.

Multiply each side of inequality in step 3 by 5.

$\begin{array}{c}\frac{x+329}{5}\cdot 5\ge 80\cdot 5\\ x+329\ge 400\end{array}$

Step 5 – Description of step.

Subtract $329$ from each side of the obtained equation.

$\begin{array}{c}x+329-329\ge 400-329\\ x\ge 71\end{array}$

Therefore, Nick must score at least 71 in the last test to receive a B in the class.