Question

the questions in the first section on a test are worth 3 points and the questions in the second section are worth 5 points. let x represent the number of correct questions from the first section, and let y represent the number of correct questions from the second section. sydney earned more than 80 points on the test. the inequality representing her score is 3x + 5y > 80. if sydney answered 15 questions in the first section correctly, what is the minimum number of questions she must have answered correctly in the second section?
options:
1
2
7
8

Explanation:

Step1: Substitute x = 15 into the inequality

We know that \( x = 15 \) (the number of correct questions in the first section). Substitute \( x = 15 \) into the inequality \( 3x + 5y>80 \). So we get \( 3\times15+5y > 80 \). Calculate \( 3\times15=45 \), then the inequality becomes \( 45 + 5y>80 \).

Step2: Solve the inequality for y

Subtract 45 from both sides of the inequality \( 45 + 5y>80 \). We have \( 5y>80 - 45 \), which simplifies to \( 5y>35 \). Then divide both sides by 5: \( y > \frac{35}{5}=7 \). Since \( y \) represents the number of correct questions (a non - negative integer), and \( y>7 \), the smallest integer value of \( y \) that satisfies this inequality is 8.

Answer:

8 (corresponding to the option "8")