Q67. - Algebra 2

Question

A test has multiple-choice questions worth 4 points each and true-false questions worth 3 points each. Marco answers 14 multiple-choice questions correctly. How many true-false questions must he answer correctly to get at least 80 points total? 

Step-by-Step Solution

Answer

Marco must answer at least 8 true-false questions correctly to get at least 80 points total.

Step 1 – State the concept

An inequality can be solved by isolating the variable on one side of the inequality.

Step 2 – List the given data

Each multiple-choice question is worth 4 points and each true-false question is worth 3 points. Marco answers 14 multiple-choice questions correctly.

Step 3 – Construct the inequality

Let Marco answer x true-false questions correctly.

 

Then, he answers 14 multiple-choice questions correctly, each worth 4 points each and x true-false questions correctly, each worth 3 points each.

 

Then his total score is $4\left(14\right)+3x$.

 

According to the problem, his total score should be at least 80.

 

Then, by the problem,

 

$4\left(14\right)+3x\ge 80$

 

This is the required inequality.

Step 4 – Solve the inequality

$4\left(14\right)+3x\ge 80$  (Obtained inequality)

 

$56+3x\ge 80$  (Simplify)

 

$56+3x-56\ge 80-56$  (Subtract 56 from both sides)

 

$3x\ge 24$ (Simplify)

 

$\frac{3x}{3}\ge \frac{24}{3}$  (Divide both sides by 3)

 

$x\ge 8$   (Simplify)

 

This implies that he must answer at least 8 true-false questions correctly to get at least 80 points total.