Joshua has to earn more than 92 points on the state test in order to qualify for an academic scholarship. Each question is worth 4 points, and the test has a total of 30 questions. Let [tex]x[/tex] represent the number of test questions.
Which of the following inequalities can be solved to determine the number of questions Joshua must answer correctly?
A. [tex]4x < 30[/tex]
B. [tex]4x < 92[/tex]
C. [tex]4x > 30[/tex]
D. [tex]4x > 92[/tex]
Answer (3)
92\ \ \ \Rightarrow\ \ \ Ans.\ d"> x − re p rese n t t h e n u mb er o f t es t q u es t i o n s 4 x − t h e n u mb er o f e a r n e d p o in t s J os h u a ha s t o e a r n m ore t han 92 p o in t s 4 x > 92 ⇒ A n s . d
The correct answer is: d. 4x > 92.
To determine the number of questions Joshua must answer correctly on the state test, we need to set up an inequality based on the scoring system described.
Each question is worth 4 points, and Joshua needs to earn more than 92 points to qualify for an academic scholarship.
Let's denote the number of questions Joshua answers correctly as x.
The total points he can earn by answering these questions correctly can be expressed as:
Total Points = 4 x
Since he needs more than 92 points, we can set up the inequality:
92"> 4 x > 92
Now, let's break down the options provided:
a. 4x < 30: This indicates that the points earned are less than 30, which is irrelevant to our requirement.
b. 4x < 92: This suggests that the points earned are less than 92, which contradicts Joshua's need to earn more than that.
c. 4x > 30: While this means he earns more than 30 points, it does not satisfy the scholarship requirement.
d. 4x > 92: This is the correct inequality reflecting that Joshua must earn more than 92 points.
To solve for x, you would divide both sides of the inequality by 4:
\frac{92}{4}"> x > 4 92 23"> x > 23
This means Joshua must answer more than 23 questions correctly to qualify for the scholarship.
Joshua must solve the inequality 92"> 4 x > 92 to determine how many questions he needs to answer correctly for the scholarship. This indicates he must answer more than 23 questions. Thus, option D is correct.
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